Related papers: Convergence of U-statistics for interacting partic…
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the…
We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or…
This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n \to \infty$ with fixed kernel size $k$. Under some regularity conditions,…
A system of N classical particles in a 2D periodic cell interacting via long-range attractive potential is studied. For low energy density $U$ a collapsed phase is identified, while in the high energy limit the particles are homogeneously…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…
In this paper we continue the study of the derivation of different types of kinetic equations which arise from scaling limits of interacting particle systems. We began this study in \cite{NVW}. More precisely, we consider the derivation of…
Bootstrap for nonlinear statistics like U-statistics of dependent data has been studied by several authors. This is typically done by producing a bootstrap version of the sample and plugging it into the statistic. We suggest an alternative…
Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
Searches for statistically significant correlations between arrival directions of ultra-high energy cosmic rays and classes of astrophysical objects are common in astroparticle physics. We present a method to test potential correlation…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain. The constants in this inequality are explicit and depend on computable bounds on the mixing rate of the…
This contribution presents a derivation of the steady-state distribution of velocities and distances of vehicles in freeway traffic which has been suggested for the evaluation of interaction potentials among vehicles (see preprint…
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…
Precise understanding of strongly interacting fermions, from electrons in modern materials to nuclear matter, presents a major goal in modern physics. However, the theoretical description of interacting Fermi systems is usually plagued by…