In this talk simple examples are presented to illustrate some aspects of random walks on groups from the point of view of probability theory, statistical physics, ergodic theory, harmonic analysis, and group theory.

p(a), 

p(a)p(b). 
p^{n}(s)= 

p(a_{n})p(a_{n1})··· p(a_{1}), 
µ_{n}^{i}= 

p^{n}(s)d_{s(ai)}, 
µ_{n}= 

p^{n}(s)d_{s}, 
H(m)= 

m(s)log(m(s)). 
D(f)(x)= 

æ ç ç è 

(  f(x+e_{i})+f(xe_{i})  ) 
ö ÷ ÷ ø 
f(x), 
Z_{n}=1+ 

e^{ia Sk}, 
l_{n}=( E  (  Z_{n}^{2}  )  )^{1/2}. 
µ_{n}= 


d_{l(a,b)(p)}. 
b(g,x)= 

(  d(g,x_{n})d(e,x_{n})  ) 
D(f)(g)= 

(  f(g a)+f(g a^{1})+f(g b)+f(g b^{1})  )  f(g), 
f(g)=  ó õ 

h_{x}(g) n(dx), 


=0. 

ó õ 

P(z,q) n(dq), 
P(z,q)= 

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