RANDOM WALKS ON THE NONNEGATIVE INTEGERS WITH A
LEFT-BOUNDED GENERATOR
Charles Delorme
Jean-Marc Rinkel
Abstract: This paper studies the random walks on the nonnegative
integers, where the ’s are independent identically distributed
random variables with generating function of type ,
a positive integer, with a convergence radius greater than . We infer from a link
between the number of zeros of inside the unit disc and a
factorisation of the symbol which allows a geometrical computation of
the potentials associated with these random walks. Examples illustrate this theory.
2000 AMS Mathematics Subject Classification: Primary: 60G50; Secondary: 47B35,
15A09, 30Cxx.
Keywords and phrases: Potentials, random walks, Toeplitz matrices.