Related papers: Large deviations of reflected weakly interacting p…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…
We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse…
We analyse large deviations of the dynamical activity in one-dimensional systems of diffusing hard particles. Using an optimal-control representation of the large-deviation problem, we analyse effective interaction forces which can be added…
The simple reflection of a light beam of finite transverse extent from a homogenous interface gives rise to a surprisingly large number of subtle shifts and deflections which can be seen as diffractive corrections to the laws of geometrical…
We study the existence and the rate of equilibration of weak solutions to a two-component system of non-linear diffusion-aggregation equations, with small cross diffusion effects. The aggregation term is assumed to be purely attractive, and…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
Weak measurements have an increasing number of applications in contemporary quantum mechanics. They were originally described as a weak interaction that slightly entangled the translational degrees of freedom of a particle to its spin,…
In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave…
We propose to use weak measurements away from the weak-value amplification regime to carry out precision measurements of time delays of light. Our scheme is robust to several sources of noise that are shown to only limit the relative…
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…
We consider a family of McKean--Vlasov equations arising as the large particle limit of a system of interacting particles on the positive half-line with common noise and feedback. Such systems are motivated by structural models for systemic…
We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…
We establish the weak large deviations principle for empirical measures of Markov chains on $\mathbb R^d$ under mild assumptions. In particular, no irreducibility is assumed and the initial measure may be arbitrary. The proof is entirely…
This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…
We study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such…
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…
We investigate a Coulomb gas in a potential satisfying a weaker growth assumption than usual and establish a large deviation principle for its empirical measure. As a consequence the empirical measure is seen to converge towards a…
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact…
Is there really such a thing as weak turbulence? Here we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence: the mutual…