Ross G. Pinsky

Learn More
spell checking I have found many more misspelled words. These and other small points of grammar have not been added to the list. Preface page iv, line-7: hardly fail to adopt it page v, line-6: before the final assault Table of Contents page viii, line 8: Erd˝ os (also in other places in the book) page viii, Stopping Times 173 page x, line 3: Carathéodory(More)
The purpose of this article is to give a rather thorough understanding of the compact support property for measure-valued processes corresponding to semi-linear equations of the form ut = Lu + βu − αu p in R u(x, 0) = f (x) in R d ; u(x, t) ≥ 0 in R d × [0, ∞). In particular, we shall investigate how the interplay between the underlying motion (the(More)
a i,j (x) ∂ 2 ∂x i ∂x j + n i=1 b i (x) ∂ ∂x i is a non-degenerate elliptic operator, g ∈ C(R n) and the reaction term f converges to −∞ at a super-linear rate as u → ∞. We give a sharp minimal growth condition on f , independent of L, in order that there exist a universal, a priori upper bound for all solutions to the above Cauchy problem—that is, in order(More)
Let D R d be an unbounded domain and let B(t) be a Brownian motion in D with normal reflection at the boundary. We study the transcience/recurrence dichotomy, focusing mainly on domains of the form D = {(x, z) ∈ R l+m : |z| < H(|x|)}, where d = l + m and H is a sufficiently regular function. This class of domains includes various horn-shaped domains and(More)
Let the random variable Z n,k denote the number of increasing subsequences of length k in a random permutation from Sn, the symmetric group of permutations of {1, ..., n}. In a recent paper [4] we showed that the weak law of large numbers holds for Z n,kn if kn = o(n 2 5); that is, lim n→∞ Z n,kn EZ n,kn = 1, in probability. The method of proof employed(More)
Consider a permutation σ ∈ S n as a deck of cards numbered from 1 to n and laid out in a row, where σ j denotes the number of the card that is in the j-th position from the left. We study some probabilistic and combina-torial aspects of the shuffle on S n defined by removing and then randomly reinserting each of the n cards once, with the removal and(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract Consider the random hypercube H n 2 (pn) obtained from the hypercube H n 2 by deleting any given edge with probabilty 1 − pn, independently of all the other edges. A diameter path in H n 2 is a longest geodesic path in H n 2. Consider the following two ways of tampering with the random graph H n 2(More)
Let D ⊂ R d be a bounded domain and denote by P(D) the space of probability measures on D. Let L = 1 2 ∇ · a∇ + b∇ be a second order elliptic operator. Let µ ∈ P(D) and δ > 0. Consider a Markov process X(t) in D which performs diffusion in D generated by the operator δL and is stopped at the boundary, and which while running, jumps instantaneously,(More)