Related papers: Distributional Response to Biases in Deterministic…
We construct both normal and anomalous deterministic biased diffusions to obtain the Einstein relation for their time-averaged transport coefficients. We find that the difference of the generalized Lyapunov exponent between biased and…
Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts…
Brownian yet non-Gaussian diffusion has recently been observed in numerous biological and active matter system. The cause of the non-Gaussian distribution have been elaborately studied in the idea of a superstatistical dynamics or a…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…
In this paper we examine the deviations from Gaussianity for two types of random variable converging to a normal distribution, namely sums of random variables generated by a deterministic discrete time map and a linearly damped variable…
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…
Weakly chaotic non-linear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and non-integrable observables remain random even in the long time limit. Temporal averages of integrable observables…
We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and…
The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…
Drift diffusion models (DDMs) have found widespread use in computational neuroscience and other fields. They model evidence accumulation in simple decision tasks as a stochastic process drifting towards a decision barrier. In models where…
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…
Motivated by applications in mathematical biology concerning randomly alternating motion of micro-organisms, we analyze a generalized integrated telegraph process. The random times between consecutive velocity reversals are…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
We establish central limit theorems for the Sample Average Approximation (SAA) method in discrete-time, finite-horizon stochastic optimal control. Our analysis is based on an abstract limit theorem for stochastic backward recursions, which…
We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are…
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a…
We develop a semiparametric framework for inference on the mean response in missing-data settings using a corrected posterior distribution. Our approach is tailored to Bayesian Additive Regression Trees (BART), which is a powerful…