Related papers: Quenched Central Limit Theorem in a Corner Growth …

In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex valued sequences. A sharp rate of…

In this paper we survey the almost sure central limit theorem and its functional form (quenched) for stationary and ergodic processes. For additive functionals of a stationary and ergodic Markov chain these theorems are known under the…

In this work we aim at proving central limit theorems for open quantum walks on $\mathbb{Z}^d$. We study the case when there are various classes of vertices in the network. Furthermore, we investigate two ways of distributing the vertex…

Let ${Z_{n},n\geq 0} $ be a critical branching process in random environment and let $T$ be its moment of extinction. Under the annealed approach we prove, as $n\to \infty ,$ a limit theorem for the number of particles in the process at…

We consider the simple random walk on random graphs generated by discrete point processes. This random graph has a random subset of a cubic lattice as the vertices and lines between any consecutive vertices on lines parallel to each…

The paper consists of two parts. In the first part we review recent work on limit theorems for random walks in random environment (RWRE) on a strip with jumps to the nearest layers. In the second part, we prove the quenched Local Limit…

Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system…

We consider the stochastic heat equation whose solution is observed discretely in space and time. An asymptotic analysis of power variations is presented including the proof of a central limit theorem. It generalizes the theory from…

In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains…

The Quantum Null Energy Condition (QNEC) relates energy to the second variation of entropy in relativistic quantum field theory. We use the QNEC inequality to bound entanglement entropy in quenches. At early times the entanglement entropy…

This thesis concerns the study of random walks in random environments (RWRE). Since there are two levels of randomness for random walks in random environments, there are two different distributions for the random walk that can be studied.…

We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability…

A short proof of the quenched central limit theorem for the random walk in random environment introduced by Boldrighini, Minlos, and Pellegrinotti is given.

We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply…

The log-partition function $ \log W_N(\beta)$ of the two-dimensional directed polymer in random environment is known to converge in distribution to a normal distribution when considering temperature in the subcritical regime…

We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random…

We prove ``effective'' linear response for certain classes of non-uniformly expanding random dynamical systems which are not necessarily composed in an i.i.d manner. In applications, the results are obtained for base maps with a sufficient…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

In this article, we investigate the asymptotic behavior of the solution to a one-dimensional stochastic heat equation with random nonlinear term generated by a stationary, ergodic random field. We extend the well-known central limit theorem…

We use martingale embeddings to prove a central limit theorem (CLT) for one-dimensional projections of high-dimensional random vectors in $\{-1,1\}^n$ satisfying a Poincar\'e inequality. We obtain a non-asymptotic error bound involving…