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UID:20250710T013233EDT-3181PzVDtv@132.216.98.100
DTSTAMP:20250710T053233Z
DESCRIPTION:Title: Random walks on simplicial complexes\n\nAbstract: \n\nMo
 tivated by the discovery of hard-to-find social networks (such as MSM or P
 WIDs) or by finding contact-tracing strategies\, we consider the question 
 of exploring the topology of random structures (such as a random graph G) 
 by random walks. The usual random walk jumps from a vertex of G to a neigh
 boring vertex\, providing information on the connected components of the g
 raph G. The number of these connected components is the Betti number beta0
 . To gather further information on the higher Betti numbers that describe 
 the topology of the graph\, we can consider the simplicial complex C assoc
 iated to the graph G: a k-simplex (edge for k=1\, triangle for k=2\, tetra
 hedron for k=3 etc.) belongs to C if all the lower (k-1)-simplices that co
 nstitute it also belong to C. For example\, a triangle belongs to C if its
  three edges are in the graph G. Several random walks have already been pr
 oposed recently to explore these structures. We introduce a new random wal
 k\, whose generator is related to a Laplacian of higher order of the graph
  and to the Betti number beta-k. A rescaling of the walk for k=2 (cycle-va
 lued random walk)\, and on regular triangulation of the torus\, is also de
 tailed. We embed the space of chains into spaces of currents to establish 
 the limiting theorem.\n\nJoint work with T. Bonis\, L. Decreusefond and Z.
  Zhang.\n
DTSTART:20221103T153000Z
DTEND:20221103T163000Z
LOCATION:Room 1214\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Chi Tran (Gustave Eiffel)
URL:/mathstat/channels/event/chi-tran-gustave-eiffel-3
 43226
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