Related papers: Quenched large deviations for interacting diffusio…
In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…
We consider a system of $N^{d}$ spins in random environment with a random local mean field type interaction. Each spin has a fixed spatial position on the torus $\mathbb{T}^{d}$, an attached random environment and a spin value in…
Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
We consider random walk with bounded jumps on a hypercubic lattice of arbitrary dimension in a dynamic random environment. The environment is temporally independent and spatially translation invariant. We study the rate functions of the…
We take the point of view of the particle in a multidimensional nearest neighbor random walk in random environment (RWRE). We prove a quenched large deviation principle and derive a variational formula for the quenched rate function. Most…
This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…
Large deviation theory (LDT) provides a mathematical framework to quantify the probabilities of rare events in stochastic systems. In this study, we applied LDT to model a chemical reaction system and demonstrated that the fluctuation…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction…
This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of…
The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random…
We establish large deviation principle (LDP) for the family of vector-valued random processes $(X^\epsilon,Y^\epsilon),\epsilon\to 0$ defined as $$ X^\epsilon_t=\frac{1}{\epsilon^\kappa}\int_0^t H(\xi^\epsilon_s,Y^\epsilon_s)ds,…
We consider the quasi-deterministic behavior of systems with a large number, $n$, of deterministically interacting constituents. This work extends the results of a previous paper [J. Stat. Phys. 99:1225-1249 (2000)] to include vector-valued…
Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…
We consider a class of particle systems described by differential equations (both stochastic and deterministic), in which the interaction network is determined by the realization of an Erd\H{o}s-R\'enyi graph with parameter $p_n\in (0, 1]$,…
We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…
In 2003, Varadhan [V03] developed a robust method for proving quenched and averaged large deviations for random walks in a uniformly elliptic and i.i.d. environment (RWRE) on $\mathbb Z^d$. One fundamental question which remained open was…
This thesis concerns the study of random walks in random environments (RWRE). Since there are two levels of randomness for random walks in random environments, there are two different distributions for the random walk that can be studied.…