Related papers: On global fluctuations for non-colliding processes
We study central limit theorems for a totally asymmetric, one-dimensional interacting random system. The models we work with are the Aldous-Diaconis-Hammersley process and the related stick model. The A-D-H process represents a particle…
The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +$\infty$) being granted by the study performed in (Chevallier, 2015), the aim of…
We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue…
The higher order moments of the fluctuations for the thermodynamical systems in the presence of fields are investigated in the framework of a theoretical method. The metod uses a generalized statistical ensemble consonant with the adequate…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
We establish limit theorems for re-scaled occupation time fluctuations of a sequence of branching particle systems in $\R^d$ with anisotropic space motion and weakly degenerate splitting ability. In the case of large dimensions, our limit…
The investigation of the behaviour for geometric functionals of random fields on manifolds has drawn recently considerable attention. In this paper, we extend this framework by considering fluctuations over time for the level curves of…
Critical phenomena arise ubiquitously in various context of physics, from condensed matter, high energy physics, cosmology, to biological systems, and consist of slow and long-distance fluctuations near a phase transition or critical point.…
We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous…
The inference of causal relationships among observed variables is a pivotal, longstanding problem in the scientific community. An intuitive method for quantifying these causal links involves examining the response of one variable to…
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics…
For large dimensional non-Hermitian random matrices $X$ with real or complex independent, identically distributed, centered entries, we consider the fluctuations of $f(X)$ as a matrix where $f$ is an analytic function around the spectrum of…
Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the…
A conditional diffusion model has been developed to analyze intricate conductance fluctuations called universal conductance fluctuations or quantum fingerprints appearing in quantum transport phenomena. The model reconstructs impurity…
We consider a class of graph-valued stochastic processes in which each vertex has a type that fluctuates randomly over time. Collectively, the paths of the vertex types up to a given time determine the probabilities that the edges are…
In this paper, we extend the fluctuation theorems used for quantum channels to multitime processes. The fluctuation theorems for quantum channels are less restrictive. We show that the given entropy production can be equal to the result of…
We consider global fluctuations of the spectrum of the GUE. Using results on the linear statistics of such matrices as well as variance bounds on the eigenvalues, we show that under a suitable scaling, global fluctuations of the spectrum…
The Gallavotti-Cohen fluctuation theorem suggests a general symmetry in the fluctuations of the entropy production, a basic concept in the theory of irreversible processes, based on results in the theory of strongly chaotic maps. We study…