Related papers: Corrections and acknowledgment for ``Local limit t…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
We consider the large deviations of the hydrodynamic rescaling of the zero-range process on $\mathbb{Z}^d$ in any dimension $d\ge 1$. Under mild and canonical hypotheses on the local jump rate, we obtain matching upper and lower bounds,…
We provide a path-wise "backbone" decomposition for supercritical superprocesses with non-local branching. Our result complements a related result obtained for super-critical superprocesses without non-local branching in [1]. Our approach…
The usable limits of the customary and relaxational filtrational theories are considered. The questions of applicable the locality and local thermodynamical equilibrium principles to depict the nonstationary flows are discussed. The…
Local terms in the Operator Product Expansion in Superconformal Theories with extended supersymmetry are identified. Assuming a factorized structure for these terms their contributions are discussed.
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
Subcritical catalytic branching random walk on d-dimensional lattice is studied. New theorems concerning the asymptotic behavior of distributions of local particles numbers are established. To prove the results different approaches are used…
An explicit solution of non-critical time-homogeneous branching processes is described.
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus…
In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…
Let (Z n) n$\ge$0 with Z n = (Z n (i, j)) 1$\le$i,j$\le$p be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method…
Correction to Annals of Probability 29 (2001) 1612--1624 [doi:10.1214/aop/1015345764].
Correction to The Annals of Statistics (2006) 34, 1013--1044 [URL: http://projecteuclid.org/euclid.aos/1151418250]
This note contains a correction to the paper, ``Local contribution to the Lefschetz fixed point formula'', Inv. Math. 111 (1993), pp. 1-33.
In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a…
The purpose of this note is to correct an error in an earlier paper by the author about the level sets of the Takagi function [Monatsh. Math. 167 (2012), 311-331 and arXiv:1102.1616], and to prove a stronger form of one of the main results…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…