Related papers: Quenched large deviations in renewal theory

Stochastic renewal processes are ubiquitous across physics, biology, and the social sciences. Here, we show that continuous-time renewal dynamics can naturally produce a mixed discrete-continuous structure, with a macroscopic fraction of…

In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…

We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\frac{d}{dt}\int\limits_0^tk(t-\tau)u(\tau)\,d\tau -k(t)u(0)$ where $k$ is a…

This article describes the quenched localisation behaviour of the Bouchaud trap model on the integers with regularly varying traps. In particular, it establishes that for almost every trapping landscape there exist arbitrarily large times…

Renewal theorems are developed for point processes with interarrival times $W_n=\xi(X_{n+1}X_n\cdots)$, where $(X_n)_{n\in\mathbb Z}$ is a stochastic process with finite state space $\Sigma$ and $\xi\colon\Sigma_A\to\mathbb R$ is a H\"older…

We present a systematic analysis of stochastic processes conditioned on an empirical measure $Q_T$ defined in a time interval $[0,T]$ for large $T$. We build our analysis starting from a discrete time Markov chain. Results for a continuous…

A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…

We prove large and moderate deviation results for sequences of compound sums, where the summands are i.i.d. random variables taking values in a separable Banach space. We establish that the results hold by proving that we are dealing with…

The guesswork problem was originally studied by Massey to quantify the number of guesses needed to ascertain a discrete random variable. It has been shown that for a large class of random processes the rescaled logarithm of the guesswork…

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…

Quenched and partially quenched chiral perturbation theory for vector mesons is developed and is used to extract chiral loop correction to the $\rho$ meson mass. Connections to fully quenched and totally unquenched chiral perturbation…

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized…

We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel…

Let $M_{l,n}$ be the number of blocks with frequency $l$ in the exchangeable random partition induced by a sample of size $n$ from the Ewens-Pitman sampling model. We show that, as $n$ tends to infinity, $n^{-1}M_{l,n}$ satisfies a large…

Let W be the number of points in (0,t] of a stationary finite-state Markov renewal point process. We derive a bound for the total variation distance between the distribution of W and a compound Poisson distribution. For any nonnegative…

The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time,…

Motivated by metastability in the zero-range process, we consider i.i.d.\ random variables with values in $\N_0$ and Weibull-like (stretched exponential) law $\mathbb P(X_i =k) = c \exp( - k^\alpha)$, $\alpha \in (0,1)$. We condition on…

Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology and economy. In this work we develop a theory for the eigenvalue fluctuations of diluted…

We study the time-dependence of the magnetization profile, m_l(t), of a large finite open quantum Ising chain after a quench. We observe a cyclic variation, in which starting with an exponentially decreasing period the local magnetization…