– It is well known that the exclusion, zero-range and misanthrope particle systems possess families of invariant measures due to the mass conservation property. Although these families have been… (More)

Preferential attachment schemes, where the selection mechanism is linear and possibly time-dependent, are considered, and an infinite-dimensional large deviation principle for the sample path… (More)

Abstract. A well-known result with respect to the one dimensional nearestneighbor symmetric simple exclusion process is the convergence to fractional Brownian motion with Hurst parameter 1/4, in the… (More)

A sequence of independent random variables {X1, X2, . . .} is called a B−harmonic Bernoulli sequence if P (Xi = 1) = 1 − P (Xi = 0) = 1/(i + B) i = 1, 2, . . ., with B ≥ 0. For k ≥ 1, the count… (More)

Consider a distinguished, or tagged particle in zero-range dynamics on Zd with rate g whose finite-range jump probabilities p possess a drift ∑ j jp(j) 6= 0. We show, in equilibrium, that the… (More)

Some growth asymptotics of a version of ‘preferential attachment’ random graphs are studied through an embedding into a continuous-time branching scheme. These results complement and extend previous… (More)

Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with nonzero drift. Let the process be stationary with product Bernoulli invariant distribution at… (More)

Large deviation results are given for a class of perturbed non-homogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {Pn}… (More)

Large deviation principles and related results are given for a class of Markov chains associated to the “leaves” in random recursive trees and preferential attachment random graphs, as well as the… (More)