Related papers: Fluctuations of particle systems determined by Sch…
We study the work fluctuations of a particle, confined to a moving harmonic potential, under the influence of friction and external Poissonian shot noise. The asymmetry of the noise induces an effective nonlinearity in the potential, which…
We establish asymptotically Gaussian fluctuations for functionals of a large class of spin models and strongly correlated random point fields, achieving near-optimal rates. For spin models, we demonstrate Gaussian asymptotics for the…
The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the…
The fluctuation theorem characterizes the distribution of the dissipation in nonequilibrium systems and proves that the average dissipation will be positive. For a large system with no external source of fluctuation, fluctuations in…
We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…
We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of $N(J)$ tends to…
We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the…
The deleting items theorems of weak law of large numbers (WLLN),strong law of large numbers (SLLN) and central limit theorem (CLT) are derived by substituting partial sum of random variable sequence with deleting items partial sum. We…
We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT). The methodology enables accurate…
The general fluctuation theory is reviewed with special attention to the role played by different ensembles, and is extended to incorporate stationary metastable states obtained in the long time limit. The fluctuation in a quantity depends…
A central limit theorem (CLT) for the smoothed empirical spectral distribution of sample covariance matrices is established. Moreover, the CLTs for the smoothed quantiles of Marcenko and Pastur's law have been also developed.
The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance.…
In this paper we present randomization methods to enhance the accuracy of the central limit theorem (CLT) based inferences about the population mean $\mu$. We introduce a broad class of randomized versions of the Student $t$-statistic, the…
We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together…
We establish a novel generalization of the fluctuation theorem for partially-masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production…
Maxwell's velocity distribution is known to be universally valid across systems and phases. Here we present a new and general derivation that uses the central limit theorem (CLT) of the probability theory. This essentially uses the idea…
We consider a random process with discrete time formed by singular values of products of truncations of Haar distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives…
Entropy and the fluctuation-dissipation theorem are at the heart of statistical mechanics near equilibrium. Driving a system beyond the linear response regime leads to (i) the breakdown of the fluctuation-dissipation theorem and (ii) a…
Ferromagnetic exponential random graph models (ERGMs) are nonlinear exponential tilts of Erd\H{o}s-R\'enyi models, under which the presence of certain subgraphs such as triangles may be emphasized. These models are mixtures of metastable…
We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…