Technion, IEM faculty - Seminar in Probability and Stochastic Processes

Speaker: Omer Angel, UBC

Title: Percolation on infinite random planar maps

Date: 06/06/2011

Time: 16:00

Place: Hashmal-861

Abstract:

A planar map is a planar graph embedded in the plane, considered up to
continuous deformations. These objects been studied extensively in
combinatorics, physics (as discrete random surfaces) and more recently
probability theory. Much progress has been made in recent years in
understanding the typical structure of these objects, and glimpses of a
deeper theory are visible, particularly connecting the scaling limit of
random planar maps with conformally invariant models of statistical
physics.

The uniform distribution on planar maps of a size $n$ converges in a
local topology as $n\to\infty$ to a limit which is a natural distribution
on infinite planar maps. I will survey some results and conjectures
concerning these objects, and discuss some recent progress in understanding
percolation on these random graphs.

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