BEGIN:VCALENDAR VERSION:2.0 PRODID:-//132.216.98.100//NONSGML kigkonsult.se iCalcreator 2.20.4// BEGIN:VEVENT 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 END:VEVENT END:VCALENDAR