Related papers: Moment bounds and concentration inequalities for s…
We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread are obtained when a given nxn complex…
Equation for anomalous diffusion in momentum space, recently obtained in the recent paper (S.A. Trigger, ArXiv 0907.2793 v1, [cond-matt. stat.-mech.], 16 July 2009) is solved for the stationary and non-stationary cases on basis of the…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…
We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and…
Eagleson's Theorem asserts that, given a probability-preserving map, ifrenormalized Birkhoff sums of a function converge in distribution, thenthey also converge with respect to any probability measure which isabsolutely continuous with…
Consider the sequence of continued fraction convergents $p_n/q_n$ to a random irrational number. We study the distribution of the sequences $p_n \pmod{m}$ and $q_n \pmod{m}$ with a fixed modulus $m$, and more generally, the distribution of…
We consider an aggregation model with nonlinear diffusion in domains with boundaries and investigate the zero diffusion limit of its solutions. We establish the convergence of weak solutions for fixed times, as well as the convergence of…
Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…
This work is a contribution to the study of the ergodic and stochastic properties of Z^d-periodic dynamical systems preserving an infinite measure. We establish functional limit theorems for natural Birkhoff sums related to local times of…
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…
We consider the coagulation dynamics A+A -> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the "anomalous kinetics" and "anomalous…
We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…
A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its…
We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
We obtain, using the Birman-Schwinger method, a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics. These conditions…