Related papers: Two-scale large deviations for chemical reaction k…
The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…
We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation…
Motivated by some numerical observations on molecular dynamics simulations, we analyze metastable trajectories in a very simplecsetting, namely paths generated by a one-dimensional overdamped Langevin equation for a double well potential.…
Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a…
A central challenge in materials science is characterizing chemical processes that are elusive to direct measurement, particularly in functional materials operating under realistic conditions. Here, we demonstrate that mechanical strain…
We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.
We study large deviations for the renormalized self-intersection local time of d-dimensional stable processes of index \beta \in (2d/3,d]. We find a difference between the upper and lower tail. In addition, we find that the behavior of the…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking…
The Brusselator model are used for the study of the intrinsic fluctuations of chemical reactions with different approaches. The equilibrium states of systems are assumed to be spirally stable in mean-field description, and two statistical…
The following question is the subject of our work: could a two-dimensional random path pushed by some constraints to an improbable "large deviation regime", possess extreme statistics with one-dimensional Kardar-Parisi-Zhang (KPZ)…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The…
Detailed balance of a chemical reaction network can be defined in several different ways. Here we investigate the relationship among four types of detailed balance conditions: deterministic, stochastic, local, and zero-order local detailed…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
An inverse problem framework for constructing reaction systems with prescribed properties is presented. Kinetic transformations are defined and analysed as a part of the framework, allowing an arbitrary polynomial ordinary differential…
We study two one-parameter families of point processes connected to random matrices: the Sine_beta and Sch_tau processes. The first one is the bulk point process limit for the Gaussian beta-ensemble. For beta=1, 2 and 4 it gives the limit…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…
We analyse dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a {\em quantum level-2.5 large deviation principle} for these systems, which describes the joint…