BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Mixing time and diameter of the percolated hypercube
DTSTART:20251128T155000
DTEND:20251128T165000
DTSTAMP:20260916T031956Z
UID:9563462002b0a642f7c3ea9ef97816d5bc1d15b43f2f551f6fcb7929
CATEGORIES:Conferences - Seminars
DESCRIPTION:Sahar Diskin (ETH Zurich)\nWe study bond percolation on the d
 -dimensional hypercube Q^d with edge retention probability p=c/d. It is
  well known that when c>1 is fixed\, a unique giant component emerges. I
 n this regime\, we resolve long-standing conjectures of Bollobás\, Kohaya
 kawa\, and Łuczak (1994) and of Benjamini and Mossel (2003)\, showing tha
 t the typical diameter of the giant component is Θ(d)\, and that the mix
 ing time of the lazy random walk on it is Θ(d^2). In the talk\, we will 
 introduce the notion of mixing time and its connection to expansion proper
 ties of subsets of the giant. We will then discuss some of the key obstacl
 es in obtaining this result\, and in particular why classical sprinkling t
 echniques are insufficient for this problem. Finally\, we will explain how
  our new approach - based on analysing the effect of small perturbations a
 nd establishing stability under thinning - overcomes these obstacles. This
  method also yields tight large-deviation estimates for the size of the gi
 ant.  \n\nBased on joint work with Michael Anastos\, Lyuben Lichev\, and
  Maksim Zhukovskii.
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR