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We study zero sets of twisted stationary Gaussian random functions on the complex plane, i.e., Gaussian random functions that are stochastically invariant under the action of the Weyl-Heisenberg group. This model includes translation…
We study the discrete Gaussian free field (harmonic crystal) on $\mathbb{Z}^d$, $d\geq 3$, with uniformly elliptic and bounded random conductances sampled according to a sufficiently mixing environment measure. We consider the hard wall…
Matrix models have phase transitions in which distributions of variables change topologically like the Gross-Witten-Wadia transition. In a recent study, similar splitting-merging behavior of distributions of dynamical variables was observed…
DP-coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvo\v{r}\'{a}k and Postle. In this paper we introduce and study the fractional DP-chromatic number $\chi_{DP}^\ast(G)$. We…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…
We study mesoscopic linear statistics for a class of determinantal point processes which interpolates between Poisson and Gaussian Unitary Ensemble statistics. These processes are obtained by modifying the spectrum of the correlation kernel…
In the last decades, various events have shown that electromechanical oscillations are a major concern for large interconnected Alternating Current (AC) power systems. Segmentation of AC power systems with High Voltage Direct Current (HVDC)…
We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…
We examine a scenario where the new physics at the LHC includes an approximate conformal field theory, where some of the degrees of freedom (aka "unparticles") carry a color charge. We present a simple argument showing that the production…
We study a distributed estimation problem in which two remotely located parties, Alice and Bob, observe an unlimited number of i.i.d. samples corresponding to two different parts of a random vector. Alice can send $k$ bits on average to…
We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on…
In this paper, we study the asymptotic relation between the maximum of acontinuous order statistics process formed by stationary Gaussian processesand the maximum of this process sampled at discrete time points. It is shown that, these two…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
Consider a graph $G$ with a coloring of its edge set $E(G)$ from a set $Q = \set{c_1,c_2, \ldots, c_q}$. Let $Q_i$ be the set of all edges colored with $c_i$. Recently, Frieze defined a notion of the perfect matching color profile denoted…
We construct a compound Poisson process conditioned on its random summation that represents the sizes of the connected components in the sparse Erd\H{o}s-R\'enyi random graph $G(n,c/n)$. This new representation depicts a connection between…
The renormalizable coloron model is built around a minimally extended color gauge group, which is spontaneously broken to QCD. The formalism introduces massive color-octet vector bosons (colorons), as well as several new scalars and…
Consider a graph $G$ and an initial random configuration, where each node is black with probability $p$ and white otherwise, independently. In discrete-time rounds, each node becomes black if it has at least $r$ black neighbors and white…
Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is…