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We develop a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic…
Recently, we proposed a method to estimate parameters of stochastic dynamics based on the linear response statistics. The method rests upon a nonlinear least-squares problem that takes into account the response properties that stem from the…
It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…
The response of physical systems to external perturbations can be used to probe both their equilibrium and non-equilibrium dynamics. While response and correlation functions are related in equilibrium by fluctuation-dissipation theorems,…
Discrete diffusion models have recently emerged as a promising alternative to the autoregressive approach for generating discrete sequences. Sample generation via gradual denoising or demasking processes allows them to capture hierarchical…
Experimental work has shown that non-equilibrium concentration fluctuations arise during free diffusion in fluids and theoretical analysis has been carried on. The results show that, in usual three-dimensional fluids, the phenomenon is…
We formulate the non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of fluctuations…
Fluctuations in nuclear collisions can be measured as a function of momentum-space binning scale over a scale interval bounded by detector two-track resolution and acceptance. Fluctuation scale dependence is related to two-particle…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
We investigate by Montecarlo simulation the linear response function of three dimensional structural glass models defined by short-range kinetic constraints and a trivial equilibrium Boltzmann-Gibbs measure. The breakdown of the…
We consider the modified Ising model introduced by de Oliveira et al. [J.Phys.A {\bf 26}, 2317 (1993)], where the temperature depends locally on the spin configuration and detailed balance and local equilibrium are not obeyed. We derive a…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized…
We study how the Einstein relation between spontaneous fluctuations and the response to an external perturbation holds in the absence of currents, for the comb model and the elastic single-file, which are examples of systems with…
A mathematical framework for the physics of nonequilibrium phenomena is gradually being developed. This review is meant to shed light on some aspects of Response Theory, on the theory of Fluctuation Relations, on the so-called "t-mixing"…
We study the linear response in different models of driven granular gases. In some situations, even if the the velocity statistics can be strongly non-Gaussian, we do not observe appreciable violations of the Einstein formula for diffusion…
In recent years, fluorescence correlation spectroscopy has been increasingly applied for the study of polymer dynamics on the nanometer scale. The core idea is to extract, from a measured autocorrelation curve, an effective mean-square…
Considering a determinantal point process on the real line, we establish a connection between the sine-kernel asymptotics for the correlation kernel and the CLT for mesoscopic linear statistics. This implies universality of mesoscopic…
We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…
The propagation of uncertainties in reaction cross sections and rates of neutron-, proton-, and $\alpha$-induced reactions into the final isotopic abundances obtained in nucleosynthesis models is an important issue in studies of…