2025




La croissance, les inégalités isopérimétriques et les fonctions harmoniques 

Lundi, ·13:30 à 15:30

Jussieu, 15-25 102

À partir de 27 janvier

   pas de cours 24 février (Congés de février du 2nd semestre)

  pas de cours 14 et 21 avril (Congés d'avril)

  L'examen lundi 12 mai

12.30 - 15-30, Salle  15-25 102


   Following preferences of  students, the course will be held in English. Please contact me if you  need some expalations about the course in French.





Topics of the course will include: isoperimetric inequalities, recurrence and transience, return probabilities and transition probabilities of the random walks.  Sobolev inequalities, Nash inequalities, long range Gaussian estimates, and inequality of Coulhon Saloff-Coste and its applications, Theorem of Pittet and Saloff-Coste about asymptotical equivalence for the return probability function 

This is also an introduction in asymptotic geometry of infinite graphs, large finite graphs, with a special interest in transitive graphes and graphes associated to  groups. The asymptotics of growth function, of isoperimetric profile and of asymptotic entropy; relation between various asymptotic invariants and their behavior for various families of graphs and groups. We will also study harmonic functions, and geometric arguments to control behavior of random walks and of discrete harmonic functions on graphs.


References


References on group theory:  Pierre de la Harpe, Topics in geometric group theory, University of Chicago Press, Chicago, IL, 2000.  



  



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