110 http://isa.epfl.ch/imoniteur_ISAP/ itffichecours.txt?path=EPFL.Etu.FicheCours.HeaderFR itffichecours.txt?path=EPFL.Etu.FicheCours.GlobalNav_js fr 2026 946228 6683147 946228 2840683608 2840683608 0 0 Systemes de communication SC IC Faculté informatique et communications School of Computer and Communication Sciences !itffichecours.htm?ww_i_matiere=2046275730&ww_x_anneeAcad=2840683608&ww_i_section=946228&ww_i_niveau=6683147 1696552884 1696552963 2025-2026 COURSE BOOKLET COM-516 Markov chains and algorithmic applications Markov chains and algorithmic applications Lecturers Lévêque Olivier, Macris Nicolas Language of teaching English Cursus Communication Systems - master program(2025-2026, SC - Master EPFL 2024)
Communication Systems - master program(2025-2026, SC - Master EPFL 2025)
Communication systems minor(2025-2026, Mineur : Systèmes de communication 2025-26)
Computer Science - Cybersecurity(2025-2026, IN-CS - Master 2024)
Computer Science - Cybersecurity(2025-2026, IN-CS - Master 2025)
Computer Science(2025-2026, IN - Master 2024)
Computer Science(2025-2026, IN - Master 2025)
Data Science(2025-2026, SC_DS - Master 2024)
Data Science(2025-2026, SC_DS - Master 2025)
Electrical Engineering (edoc)(2025-2026, EDEE 2025-26)
SemesterMand.OptionFilières
x
Hx
MA1, MA3x
MA1, MA3xB I M
MA1, MA3xB I
 Credits 6 Session Winter Workload 180h Exam Written Number of positions Semester Fall Weeks 14 Hours 4 weekly
Courses 2 weekly
Exercises 1 weekly
Lab 1 weekly
Study planSemesterMand.OptionFilières
Cyber security 2025-26MA1x
Cyber security 2025-26MA3x
Data Science 2025-26MA1x
Data Science 2025-26MA3x
EDEE - Electrical Engineering 2025-26x
Informatique 2025-26MA1xB I M
Informatique 2025-26MA3xB I M
Mineur : Systèmes de communication 2025-26Hx
Systèmes de communication 2025-26MA1xB I
Systèmes de communication 2025-26MA3xB I
Cursus Sem. Type
Communication systems minor H Opt.
Computer science MA1, MA3 Opt.
Cybersecurity MA1, MA3 Opt.
Data Science MA1, MA3 Opt.
Electrical Engineering Opt.
SC master EPFL MA1, MA3 Opt.
Remark Cours biennal Summary The study of random walks finds many applications in computer science and communications. The goal of the course is to get familiar with the theory of random walks, and to get an overview of some applications of this theory to problems of interest in communications, computer and network science. Content

Part 1: Markov chains (~6 weeks):

- basic properties: irreducibility, periodicity, recurrence/transience, stationary and limiting distributions,

- ergodic theorem: coupling method

- detailed balance

- convergence rate to the equilibrium, spectral gap, mixing times

- cutoff phenomenon

Part 2: Sampling (~6 weeks)

- classical methods, importance and rejection sampling

- Markov Chain Monte Carlo methods, Metropolis-Hastings algorithm, Glauber dynamics, Gibbs sampling

- applications: function minimization, coloring problem, satisfiability problems, Ising models

- coupling from the past and exact simulation

 Keywords

random walks, stationarity, ergodic, convergence, spectral gap, mixing time, sampling, Markov chain Monte Carlo, coupling from the past

 Learning Prerequisites Required courses

Basic probability course

Basic linear algebra and calculus courses

 Recommended courses

Stochastic Models for Communications (COM-300)

 Important concepts to start the course

Good knowledge of probability and analysis.

Having been exposed to the theory of Markov chains.

 Learning Outcomes By the end of the course, the student must be able to:
  • Analyze the behaviour of a random walk
  • Assess / Evaluate the performance of an algorithm on a graph
  • Implement efficiently various sampling methods
 Teaching methods

ex-cathedra course

 Expected student activities

active participation to exercise sessions and implementation of a sampling algorithm

 Assessment methods

midterm (15%), mini-project (15%), final exam (70%)

 Resources Bibliography

Various references will be given to the students during the course, according to the topics discussed in class.

 Ressources en bibliothèque
  • Probability and random processes / Grimmetthttp://library.epfl.ch/en/beast?isbn=9780198572237
 Notes/Handbook

Lecture notes will be provided

 Websites Moodle Link Prerequisite for

This course is not so to speak a prerequisite for other courses, but could complement well the course COM-512 on Networks out of control, as well as other courses in statistics.

 Systèmes de communication - master, 2025-2026, Master semestre 1 Communication Systems - master program, 2025-2026, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 1 MA1 HIVER Master semester 1 MA1 Systèmes de communication - master SC_EPFL Communication Systems - master program SC_EPFL
Systèmes de communication SC Communication Systems SC
B I optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Systèmes de communication - master, 2025-2026, Master semestre 3 Communication Systems - master program, 2025-2026, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 3 MA3 HIVER Master semester 3 MA3 Systèmes de communication - master SC_EPFL Communication Systems - master program SC_EPFL
Systèmes de communication SC Communication Systems SC
B I optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Data Science, 2025-2026, Master semestre 1 Data Science, 2025-2026, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 1 MA1 HIVER Master semester 1 MA1 Data Science SC_DS Data Science SC_DS
Systèmes de communication SC Communication Systems SC
optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Data Science, 2025-2026, Master semestre 3 Data Science, 2025-2026, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 3 MA3 HIVER Master semester 3 MA3 Data Science SC_DS Data Science SC_DS
Systèmes de communication SC Communication Systems SC
optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Informatique - Cybersecurity, 2025-2026, Master semestre 1 Computer Science - Cybersecurity, 2025-2026, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 1 MA1 HIVER Master semester 1 MA1 Informatique - Cybersecurity IN_CS Computer Science - Cybersecurity IN_CS
Informatique IN Computer Science IN
optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Informatique - Cybersecurity, 2025-2026, Master semestre 3 Computer Science - Cybersecurity, 2025-2026, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 3 MA3 HIVER Master semester 3 MA3 Informatique - Cybersecurity IN_CS Computer Science - Cybersecurity IN_CS
Informatique IN Computer Science IN
optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Informatique, 2025-2026, Master semestre 1 Computer Science, 2025-2026, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 1 MA1 HIVER Master semester 1 MA1 Informatique IN Computer Science IN
Informatique IN Computer Science IN
B I M optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Informatique, 2025-2026, Master semestre 3 Computer Science, 2025-2026, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 3 MA3 HIVER Master semester 3 MA3 Informatique IN Computer Science IN
Informatique IN Computer Science IN
B I M optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Génie électrique (edoc), 2025-2026 Electrical Engineering (edoc), 2025-2026 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Génie électrique (edoc) EDEE Electrical Engineering (edoc) EDEE
optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
Mineur en Systèmes de communication, 2025-2026, Semestre automne Communication systems minor, 2025-2026, Autumn semester Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Semestre automne H HIVER Autumn semester H Mineur en Systèmes de communication MIN_SC Communication systems minor MIN_SC
optionnel optional
2 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Exercices Exercises Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
1 Labo Lab Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Macris Nicolas 107423
Systèmes de communication SC Communication Systems SC
Lévêque Olivier 107931
Systèmes de communication SC Communication Systems SC
Cours biennal 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications 6
Ecrit Written Crédit Credits 6 Session hiver Session winter HIV HIV
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FO_fin HTML_debut &#948; HTML_fin JS_debut \x26#948; JS_fin CODE56073309 BOOLEAN_Symbol 1 BaliseJS_debut \x5bpi\x5d BaliseJS_fin Balise_debut [pi] Balise_fin FO_debut [inline]=&#960; FO_fin HTML_debut &#960; HTML_fin JS_debut \x26#960; JS_fin CODE56074095 BOOLEAN_Symbol 1 BaliseJS_debut \x5bDELTA\x5d BaliseJS_fin Balise_debut [DELTA] Balise_fin FO_debut [inline]=&#916; FO_fin HTML_debut &#916; HTML_fin JS_debut \x26#916; JS_fin CODE56074172 BOOLEAN_Symbol 1 BaliseJS_debut \x5bMU\x5d BaliseJS_fin Balise_debut [MU] Balise_fin FO_debut [inline]=&#924; FO_fin HTML_debut &#924; HTML_fin JS_debut \x26#924; JS_fin CODE56074264 BOOLEAN_Symbol 1 BaliseJS_debut \x5bPI\x5d BaliseJS_fin Balise_debut [PI] Balise_fin FO_debut [inline]=&#928; FO_fin HTML_debut &#928; HTML_fin JS_debut \x26#928; JS_fin CODE56074328 BOOLEAN_Symbol 1 BaliseJS_debut \x5bSIGMA\x5d BaliseJS_fin Balise_debut [SIGMA] Balise_fin FO_debut [inline]=&#931; FO_fin HTML_debut &#931; HTML_fin JS_debut \x26#931; JS_fin CODE56075056 BOOLEAN_Symbol 1 BaliseJS_debut \x5bALPHA\x5d BaliseJS_fin Balise_debut [ALPHA] Balise_fin FO_debut [inline]=&#913; 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FO_fin HTML_debut &#951; HTML_fin JS_debut \x26#951; JS_fin CODE72092805 BOOLEAN_Symbol BaliseJS_debut \x5bETA\x5d BaliseJS_fin Balise_debut [ETA] Balise_fin FO_debut [inline]=&#919; FO_fin HTML_debut &#919; HTML_fin JS_debut \x26#919; JS_fin BALISE_SOULIGNER BOOLEAN_Symbol BaliseJS_debut \x5bu\x5d BaliseJS_fin \x5b\x2fu\x5d Balise_debut [u] Balise_fin [/u] FO_debut text-decoration=underline FO_fin text-decoration=none HTML_debut <u> HTML_fin </u> JS_debut \x3cu\x3e JS_fin \x3c\x2fu\x3e CODE72092388 BOOLEAN_Symbol BaliseJS_debut \x5bpsi\x5d BaliseJS_fin Balise_debut [psi] Balise_fin FO_debut [inline]=&#968; FO_fin HTML_debut &#968; HTML_fin JS_debut \x26#968; JS_fin CODE72092541 BOOLEAN_Symbol BaliseJS_debut \x5bPSI\x5d BaliseJS_fin Balise_debut [PSI] Balise_fin FO_debut [inline]=&#936; FO_fin HTML_debut &#936; HTML_fin JS_debut \x26#936; JS_fin CODE140502511 BOOLEAN_Symbol 1 BaliseJS_debut \x5brho\x5d BaliseJS_fin Balise_debut [rho] Balise_fin FO_debut [inline]=&#961; FO_fin HTML_debut &#961; HTML_fin JS_debut \x26#961; JS_fin CODE140504636 BOOLEAN_Symbol 1 BaliseJS_debut \x5bRHO\x5d BaliseJS_fin Balise_debut [RHO] Balise_fin FO_debut [inline]=&#929; FO_fin HTML_debut &#929; HTML_fin JS_debut \x26#929; JS_fin CODE148292791 BOOLEAN_Symbol BaliseJS_debut \x5bepsilon\x5d BaliseJS_fin Balise_debut [epsilon] Balise_fin FO_debut [inline]=&#949; FO_fin HTML_debut &#949; HTML_fin JS_debut \x26#949; JS_fin CODE169976220 BOOLEAN_Symbol BaliseJS_debut \x5blig\x5d BaliseJS_fin Balise_debut [lig] Balise_fin FO_debut [inline]=&#x203A;&#160;&#160; FO_fin HTML_debut &#x203A;&#160;&#160; HTML_fin JS_debut \x26#x203A;\x26#160;\x26#160; JS_fin CODE148292899 BOOLEAN_Symbol BaliseJS_debut \x5bEPSILON\x5d BaliseJS_fin Balise_debut [EPSILON] Balise_fin FO_debut [inline]=&#917; FO_fin HTML_debut &#917; HTML_fin JS_debut \x26#917; JS_fin BALISETXT_SAUT BOOLEAN_Symbol BaliseJS_debut \x5bbr\x2f\x5d BaliseJS_fin Balise_debut [br/] Balise_fin FO_debut FO_fin HTML_debut <br/> HTML_fin JS_debut \x3cbr\x2f\x3e JS_fin 2046275730 Markov chains and algorithmic applications Markov chains and algorithmic applications anglais Lévêque Olivier 107931 Macris Nicolas 107423 950840