Abstract. Invariance principle in L(0, 1) is studied using signed random measures. This approach to the problem uses an explicit isometry between L(0, 1) and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a L(0, 1) version of the invariance principle in the case of...

The universal dynamic and static properties of two dimensional antiferromagnets in the vicinity of a zero-temperature phase transition from long-range magnetic order to a quantum disordered phase are studied. Random antiferromagnets with both Néel and spin-glass longrange magnetic order are considered. Explicit quantum-critical dynamic scaling functions are computed in a 1/N expansion to two-lo...

We formulate PRNU-based image manipulation localization as a probabilistic binary labeling task in a flexible discriminative random field (DRF) framework. A novel local discriminator based on the deviation of the measured correlation from the expected local correlation as estimated by a correlation predictor is paired with an explicit pairwise model for dependencies between local decisions. Exp...

Random graphs with high probability satisfy the n-e.c. adjacency property, although until recently few explicit examples of such graphs were known. We supply a new general construction for generating infinite familes of finite regular n-e.c. graphs derived from certain resolvable Steiner 2-designs. We supply an extension of our construction to the infinite case, and thereby give a new represent...

We consider a stochastic SIS infection model for a population partitioned into m households assuming random mixing. We solve the model in the limit m --> infinity by using the self-consistent field method of statistical physics. We derive a number of explicit results, and give numerical illustrations. We then do numerical simulations of the model for finite m and without random mixing. We find ...

The explicit form of L evy measure for geometric stable (GS) random variables follows from the general L evy{Kchintchine representation of a subordinated innnitely di-visible process. Through this form, asymptotic properties of L evy measure are studied. In particular, logarithmic asymptotics around the origin imply exponential rate of convergence in series representation of GS random variables...

We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically, and explicit calculations are performed for the two-point correlation function. This problem naturally appears in, e.g., rank-1 perturbation of an integrable Hamiltonian and, in ...

We introduce a method to prove metastability of the contact process on Erdős–Rényi graphs and configuration model graphs. The relies uniformly bounding total infection rate from below, over all sets with fixed number nodes. Once this bound is established, simple comparison well chosen birth-and-death will show exponential growth extinction time. Our paper complements recent results process: und...

In this paper we study inverting random functions under the maximum likelihood estimation (MLE) criterion in the discrete setting. In particular, we consider how many independent evaluations of the random function at a particular element of the domain are needed for reliable reconstruction of that element. We provide explicit upper and lower bounds for MLE, both in the nonparametric and paramet...

We consider the asymptotics of the second-order correlation function of the characteristic polynomial of a random matrix. We show that the known result for a random matrix from the Gaussian Unitary Ensemble essentially continues to hold for a general Hermitian Wigner matrix. Our proofs rely on an explicit formula for the exponential generating function of the second-order correlation function o...