Search
Now showing items 17 of 7

On the spectrum and Martin boundary of homogeneous spaces
(Statistics and Probability Letters, 1995)Given a conservative, spatially homogeneous Markov process X on an homogeneous spaces χ, we show that if the bottom of the spectrum of the generator of X is zero then the Martin boundary of contains a unique point fixed ... 
On the Commute Time of Random Walks on Graphs
(Brazilian Journal of Probability and Statistics, 1995)Given a simple random walk on an undirected connected graph, the commute time of the vertices x and y is defined as C(x,y) = ExTy+EyTx. We give a new proof, based on the optional sampling theorem for martingales, of the ... 
On Iterates of Moebius transformations on fields
(Mathematics of Computation, 1997)Let p be a quadratic polynomial over a splitting field K, and S be the set of zeros of p. We define an associative and commutative binary relation on G ≡ K ∪ {∞ } S so that every Moebius transformation with fixed point ... 
A note on the Zeta Function of a Graph
(Journal of Combinatorial Theory Series B, 1998)The number of splanning trees in a finite graph is first expressed as the derivative (at 1) of a determinant and then in terms of a zeta function. This generalizes a result of Hashimoto to nonregular graphs. 
Amenability and superharmonic functions
(Proceedings of the American Mathematical Society, 1993)Let G be a countable group and u a symmetric and aperiodic probability measure on G . We show that G is amenable if and only if every positive superharmonic function is nearly constant on certain arbitrarily large subsets ... 
Geodesics and Bounded Harmonic Functions on Infinite Graphs
(1991)It is shown there that an infinite connected planar graph with a uniform upper bound on vertex degree and rapidly decreasing Green's function (relative to the simple random walk) has infinitely many pairwise finitelyintersecting ... 
Cogrowth of Regular Graphs
(Proceedings of the American Mathematical Society, 1992)Let G be a dregular graph and T the covering tree of G. We define a cogrowth constant of G in T and express it in terms of the first eigenvalue of the Laplacian on G. As a corollary, we show that the cogrowth constant is ...