Related papers: Stationary fluctuations for a multi-species zero r…
The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
Consider Dyson's Hermitian Brownian motion model after a finite time S, where the process is started at N equidistant points on the real line. These N points after time S form a determinantal process and has a limit as N tends to infinity.…
Conjecture II.3.6 of Spohn in [Spohn '91] and Lecture 7 of Jensen-Yau in [Jensen-Yau '99] ask for a general derivation of universal fluctuations of hydrodynamic limits in large-scale stochastic interacting particle systems. However, the…
We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by…
We consider the one-dimensional stirring process on the segment $\{-N,\ldots,N\}$, coupled to boundary dynamics that inject particles from the right reservoir and remove particles from the left reservoir, each acting on a window of size…
We study negative large deviations of the long-time empirical front velocity of the center of mass of the one-sided $N$-BBM ($N$-particle branching Brownian motion) system in one dimension. Employing the macroscopic fluctuation theory, we…
We introduce and study a new class of fronts in finite particle number reaction-diffusion systems, corresponding to propagating up a reaction rate gradient. We show that these systems have no traditional mean-field limit, as the nature of…
We study analytically the distribution of fluctuations of the quantities whose average yield the usual two-point correlation and linear response functions in three unfrustrated models: the random walk, the $d$ dimensional scalar field and…
A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on…
We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can…
The equation of state with quantum statistics corrections is used for particle number fluctuations $\omega$ of isotopically symmetric nuclear matter with interparticle van der Waals and Skyrme local density interactions. The fluctuations,…
We develop a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic…
Heat fluctuations are studied in a dissipative system with both mechanical and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extended stationary state fluctuation theorem is…
We introduce a new class of stochastic processes which are stationary, Markovian and characterized by an infinite range of time-scales. By transforming the Fokker-Planck equation of the process into a Schrodinger equation with an…
We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of…
From the events generated from the MC code of a multi-phase transport (AMPT) model with string melting, the properties of multiplicity fluctuations of charged particles in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=\rm{~2.76 \,TeV}$ are…
We consider a directed abelian sandpile on a strip of size $2\times n$, driven by adding a grain randomly at the left boundary after every $T$ time-steps. We establish the exact equivalence of the problem of mass fluctuations in the steady…
We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x) = \alpha \, |x|^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$…
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…