401-4597-67L  Probability on Transitive Graphs

SemesterAutumn Semester 2017
LecturersV. Tassion
Periodicitynon-recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-4597-67 VProbability on Transitive Graphs2 hrs
Tue15:15-17:00HG E 33.1 »
V. Tassion

Catalogue data

AbstractIn this course, we will present modern topics at the interface between probability and geometric group theory. We will define two random processes on Cayley graphs: the simple random walk and percolation, and discuss their respective behaviors depending on the geometric properties of the underlying group.
ObjectivePresent in an original framework important tools in the study of
- random walks: spectral gap, harmonic functions, entropy,...
- percolation: uniqueness of the infinite cluster, mass-transport principle,...
ContentIn this course, we will present modern topics at the interface between probability and geometric group theory. To every group with a finite generating set, one can associate a graph, called Cayley graph. (For example, the d-dimensional grid is a Cayley graph associated to the group Z^d.) Then, we will define two random processes on Cayley graphs: the simple random walk and percolation, and discuss their respective behaviors depending on the geometric properties of the underlying group. The focus will be on the random processes and their properties, and we will use very few notions of geometric group theory.
LiteratureProbability on trees and network (R. Lyons, Y. Peres)
Prerequisites / Notice- Probability Theory
- No prerequisite on group theory, all the background will be introduced in class.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersV. Tassion
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

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Groups

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Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics MasterSelection: Probability Theory, StatisticsWInformation