If G is an infinite graph with bounded degree, this talk analyzes the relations between the asymptotic behavior of a nearest neighbor Markov chain on the graph and some simple geometric characteristics of the graph.
Ñ f(x)= 
æ ç ç ç ç è 

ó õ 

f(x)f(y)^{2}p(x,y) 
ö ÷ ÷ ÷ ÷ ø 

, 
A 

£ C 

µ_{xy}, 
c'k^{D/2}£ 

p^{2k}(x,x)£ C'k 

, 
p^{k}(x,y)£ C 

exp 
æ ç ç è 
c 

ö ÷ ÷ ø 
" x,yÎ G, k³1. (UE) 
p^{2k}(x,y)³ c 

" xÎ G, k³1. (DLE) 
inf  {   Ñ f_{2}^{2};fÎ c_{0}(A), f_{2}=1  }  ³ 

æ ç ç è 

ö ÷ ÷ ø 

, (FK) 
This document was translated from L^{A}T_{E}X by H^{E}V^{E}A.