We consider a class of pure jump Markov processes in R whose jump kernels are comparable to those of symmetric stable processes. We establish a Harnack inequality for nonnegative functions that are… (More)

We consider symmetric Markov chains on the integer lattice in d dimensions, where α ∈ (0, 2) and the conductance between x and y is comparable to |x−y|−(d+α). We establish upper and lower bounds for… (More)

Consider a sequence {Xi(0)}i=1 of i.i.d. random variables. Associate to each Xi(0) an independent mean-one Poisson clock. Every time a clock rings replace that X-variable by an independent copy and… (More)

A. We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie-Weiss Model. For β < 1, we prove that the dynamics exhibits a cut-o ff: the distance to… (More)

Unlike most books reviewed in the Intelligencer this is definitely a textbook. It assumes knowledge one might acquire in the first two years of an undergraduate mathematics program – basic… (More)

Let V denote a set of N vertices. To construct a hypergraph process, create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random, with generating… (More)

Fusion has become the standard of care for numerous pathologic conditions of the spine over the past 50 years. Instrumented thoracolumbar fusion for adolescent and adult spinal deformity has enjoyed… (More)

In this paper, we study a family of lattice walks which are related to the Hadamard conjecture. There is a bijection between paths of these walks which originate and terminate at the origin and… (More)