This paper studies heavy traffic behavior of a G/G/1 last-in-first-out (LIFO) preemptive resume queue, by extending the techniques developed in Limic (1999). The queue length process exhibits a perhaps unexpected heavy traffic behavior. The diffusion limit depends on the type…

This paper provides transition probability estimates of transient reversible Markov chains. The key condition of the result is the spatial symmetry and polynomial decay of the Green's function of the chain.

We establish a formula for the distribution of loop-erased random walks at certain random times. Several classical results on spanning trees, including Wilson's algorithm, follow easily, as well as a method to construct random Hamiltonian cycles.

We determine the law of the convex minorant $(M_s, s\in [0,1])$ of a real-valued Cauchy process on the unit time interval, in terms of the gamma process. In particular, this enables us to deduce that the paths of $M$ have…

Given a standard Brownian motion $B$, we show that the equation $$ X_t = x_0 + B_t + \beta(L_t^X), t \geq 0,$$ has a unique strong solution $X$. Here $L^X$ is the symmetric local time of $X$ at $0$, and…

Let $B(t)$ denote Brownian motion in $R^d$. It is a classical fact that for any Borel set $A$ in $R^d$, the volume $V_1(A)$ of the Wiener sausage $B[0,1]+A$ has nonzero expectation iff $A$ is nonpolar. We show that for any…

In this article we consider the sample covariance matrix formed from a sequence of independent and identically distributed random vectors from the generalized domain of attraction of the multivariate normal law. We show that this sample covariance matrix, appropriately normalized…

We provide a simple probabilistic proof of a result of J. Král and I. Netuka: If  $f$ is a measurable real-valued function on $\mathbb{R}^d$ ($d > 1$) then the set of points at which  $f$ has a strict fine local…

The weak limit of the normalized number of comparisons needed by the Quicksort algorithm to sort n randomly permuted items is known to be determined implicitly by a distributional fixed-point equation. We give an algorithm for perfect random variate generation…

We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply in particular to non-Gaussian Wigner and Wishart matrices. We also provide concentration bounds…