Related papers: Gaussian fluctuations for interacting particle sys…
Particle number fluctuations are considered within the van der Waals (VDW) equation, which contains both attractive (mean-field) and repulsive (eigenvolume) interactions. The VDW equation is used to calculate the scaled variance of particle…
Based on the canonical ensemble, we suggested the simple scheme for taking into account Gaussian fluctuations in a finite system of ideal boson gas. Within framework of scheme we investigated the influence of fluctuations on the particle…
The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with…
For the Moran model with strong or moderately strong selection we prove that the fluctuations around the deterministic limit of the line counting process of the ancestral selection graph converge to an Ornstein-Uhlenbeck process. To this…
The Gaussian Orthogonal Ensemble (GOE) of random matrices has been widely employed to describe diverse phenomena in strongly coupled quantum systems. An important prediction is that the decay rates of the GOE eigenstates fluctuate according…
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…
We study the fluctuations of the outer domain of Hastings-Levitov clusters in the small particle limit. These are shown to be given by a continuous Gaussian process $\mathcal{F}$ taking values in the space of holomorphic functions on $\{…
We have investigated by molecular dynamics method the influence of a finite number of particles used in computer simulations on fluctuations of thermodynamic properties. As a case study, we used the two-dimensional Lennard-Jones system. 2D…
We analyze nonequilibrium fluctuations of the averaging process on $\mathbb T_\varepsilon^d$, a continuous degenerate Gibbs sampler running over the edges of the discrete $d$-dimensional torus. We show that, if we start from a smooth…
A stochastic process with self-interaction as a model of quantum field theory is studied. We consider an Ornstein-Uhlenbeck stochastic process x(t) with interaction of the form x^{(\alpha)}(t)^4, where $\alpha$ indicates the fractional…
We study the fluctuation behavior of individual eigenvalues of kernel matrices arising from dense graphon-based random graphs. Under minimal integrability and boundedness assumptions on the graphon, we establish distributional limits for…
We revisit the large-scale Gaussian fluctuations for the stochastic Landau-Lifshitz Navier-Stokes equation (LLNS) at and above criticality, using the method in \cite{CGT24}. With the classical diffusive scaling in $d\geq 3$ and weak…
We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…
We study a sequential system of interacting diffusions in which particle $i$ interacts only with its predecessors through the empirical measure $\mu_t^{i-1}$, yielding a directed, non-exchangeable mean-field approximation of a…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…
We show, for a class of discrete Fleming-Viot (or Moran) type particle systems, that the convergence to the equilibrium is exponential for a suitable Wassertein coupling distance. The approach provides an explicit quantitative estimate on…
We study long time behavior of a discrete time weakly interacting particle system, and the corresponding nonlinear Markov process in $\mathbb{R}^d$, described in terms of a general stochastic evolution equation. In a setting where the state…
Fluctuations of the number of particles for the dilute interacting gas with Bose-Einstein condensate are considered. It is shown that in the Bogolubov theory these fluctuations are normal. The fluctuations of condensed as well as…
We propose a transfer principle to study the adapted 2-Wasserstein distance between stochastic processes. First, we obtain an explicit formula for the distance between real-valued mean-square continuous Gaussian processes by introducing the…