A description of the martin boundary for nearest neighbour random walks on free products

1986 ◽  
pp. 203-215 ◽  
Author(s):  
Wolfgang Woess
Keyword(s):  
Random Walks ◽  
Martin Boundary ◽  
Nearest Neighbour ◽  
Free Products

The almost sure central limit theorem for one-dimensional nearest-neighbour random walks in a space-time random environment

2004 ◽  
Vol 41 (01) ◽  
pp. 83-92 ◽  
Author(s):  
Jean Bérard
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Random Environment ◽  
Space Time ◽  
Nearest Neighbour ◽  
One Dimensional ◽  
The Central Limit Theorem ◽  
Almost All

The central limit theorem for random walks on ℤ in an i.i.d. space-time random environment was proved by Bernabeiet al.for almost all realization of the environment, under a small randomness assumption. In this paper, we prove that, in the nearest-neighbour case, when the averaged random walk is symmetric, the almost sure central limit theorem holds for anarbitrarylevel of randomness.

Random walks and periodic continued fractions

1985 ◽  
Vol 17 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Wolfgang Woess
Keyword(s):  
Random Walks ◽  
Harmonic Functions ◽  
Limit Theorems ◽  
Continued Fraction ◽  
Transition Probabilities ◽  
Local Limit ◽  
Periodic Sequence ◽  
Nearest Neighbour ◽  
Continued Fraction Expansions ◽  
Local Limit Theorems

Nearest-neighbour random walks on the non-negative integers with transition probabilities p0,1 = 1, pk,k–1 = gk, pk,k+1 = 1– gk (0 < gk < 1, k = 1, 2, …) are studied by use of generating functions and continued fraction expansions. In particular, when (gk) is a periodic sequence, local limit theorems are proved and the harmonic functions are determined. These results are applied to simple random walks on certain trees.

scholarly journals Branching random walks on free products of groups

2012 ◽  
Vol 104 (6) ◽  
pp. 1085-1120 ◽  
Author(s):  
Elisabetta Candellero ◽  
Lorenz A. Gilch ◽  
Sebastian Müller
Keyword(s):  
Random Walks ◽  
Free Products ◽  
Branching Random Walks ◽  
Products Of Groups

On a class of two-dimensional nearest-neighbour random walks

1994 ◽  
Vol 31 (A) ◽  
pp. 207-237 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Random Walks ◽  
State Space ◽  
Generating Function ◽  
The State ◽  
Nearest Neighbour ◽  
North East ◽  
The North ◽  
One Step ◽  
Bivariate Generating Function ◽  
Positive Recurrent

For positive recurrent nearest-neighbour, semi-homogeneous random walks on the lattice {0, 1, 2, …} X {0, 1, 2, …} the bivariate generating function of the stationary distribution is analysed for the case where one-step transitions to the north, north-east and east at interior points of the state space all have zero probability. It is shown that this generating function can be represented by meromorphic functions. The construction of this representation is exposed for a variety of one-step transition vectors at the boundary points of the state space.

Random walks and periodic continued fractions

1985 ◽  
Vol 17 (01) ◽  
pp. 67-84 ◽  
Author(s):  
Wolfgang Woess
Keyword(s):  
Random Walks ◽  
Harmonic Functions ◽  
Limit Theorems ◽  
Continued Fraction ◽  
Transition Probabilities ◽  
Local Limit ◽  
Periodic Sequence ◽  
Nearest Neighbour ◽  
Continued Fraction Expansions ◽  
Local Limit Theorems

Nearest-neighbour random walks on the non-negative integers with transition probabilitiesp0,1= 1,pk,k–1=gk,pk,k+1= 1–gk(0 &lt;gk&lt; 1,k= 1, 2, …) are studied by use of generating functions and continued fraction expansions. In particular, when (gk) is a periodic sequence, local limit theorems are proved and the harmonic functions are determined. These results are applied to simple random walks on certain trees.

scholarly journals Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Lorenz A. Gilch
Keyword(s):  
Random Walks ◽  
Finite Groups ◽  
Transition Probabilities ◽  
Finite Alphabet ◽  
Free Products ◽  
Rate Of Escape ◽  
International Audience ◽  
Special Case ◽  
Current Word ◽  
Natural Way

International audience We consider random walks on the set of all words over a finite alphabet such that in each step only the last two letters of the current word may be modified and only one letter may be adjoined or deleted. We assume that the transition probabilities depend only on the last two letters of the current word. Furthermore, we consider also the special case of random walks on free products by amalgamation of finite groups which arise in a natural way from random walks on the single factors. The aim of this paper is to compute several equivalent formulas for the rate of escape with respect to natural length functions for these random walks using different techniques.

Sign in / Sign up

Export Citation Format

Share Document