05.07.22

Jean Lecureux (Université Paris-Saclay)

Title

Random walks on CAT(0) cubical complexes

Abstract

Let X be a CAT(0) cubical complex and G be a group acting on X. Pick independent random variables g_i in G, with the same law. The associated random walk is then the product Z_n = g₁g₂ ... g_n. Choosing some origin o in X, we study the asymptotic behavior of the sequence (Z_n o). More precisely, we prove that (almost surely) d(Z_n o,o) is equivalent to nA for some A>0, and that (Z_n o) converges to a point in the (suitably defined) boundary  of X. We also prove a Central Limit Theorem : the quotient d(Z_no,o)-nA/\sqrt n converges (in law) to a non-degenerate Gaussian law. This is a joint work with Talia Fernós and Frédéric Mathéus.

Schedule

10:00 - 11:30 RTG Lecture 1 (Max Riestenberg), SR 2.058

11:30 - 12:00 Get-Together with speaker, SR2.058

12:00 - 13:00 Common lunch

13:00 - 13:30 Informal meeting of PhD students, Topologischer Raum

13:45 - 14:45 RTG colloquium: Jean Lecureux, SR. 1067

14:45 - 15:30 Common tea, Faculty meeting room 1.058

15:30 - 17:00 RTG Lecture 3 (Alexander Lytchak), SR 1.067

KIT