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Now showing items 1-7 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 ...

#### 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 ...

#### 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 ...

#### 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 finitely-intersecting ...

#### 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 ...

#### Cogrowth of Regular Graphs

(Proceedings of the American Mathematical Society, 1992)

Let G be a d-regular 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 ...

#### 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 non-regular graphs.