Collisions of Independent Random Walks in Infinite Graphs

Koops, Wietze (2020) Collisions of Independent Random Walks in Infinite Graphs. Bachelor's Thesis, Mathematics.

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Abstract

A recurrent graph has the (in)finite collision property if two independent random walks started from the same point collide (in)finitely often almost surely. Krishnapur and Peres (2004) show that the graph Comb(Z), which is obtained from the integer lattice Z^2 by removing all horizontal edges not on the x-axis, is a recurrent graph with the finite collision property. Barlow, Peres and Sousi (2012) further study the collision properties of power-law combs, subgraphs of Comb(Z) where all vertices (x, y) where y is smaller than 0 or larger than f(x) and the corresponding edges are removed. In this thesis, these results are explained in detail. Finally, the case where the heights f(n) of the comb graph are i.i.d. random variables with a given law is considered. In particular a condition on this law is given, which implies that the resulting comb graph has the finite collision property.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Rodrigues Valesin, D. and Hirsch, C.P.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	02 Aug 2020 10:28
Last Modified:	02 Aug 2020 10:28
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/22958

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