Related papers: Maximal Inequalities for Empirical Processes under…

We prove a strong law of large numbers for a class of strongly mixing processes. Our result rests on recent advances in understanding of concentration of measure. It is simple to apply and gives finite-sample (as opposed to asymptotic)…

The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…

We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…

Slow mixing is the central hurdle when working with Markov chains, especially those used for Monte Carlo approximations (MCMC). In many applications, it is only of interest to estimate the stationary expectations of a small set of…

Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize and ultimately reach a uniform state. However, this scenario only holds when the…

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…

The paper considers two main results. First one is the uniform bound for strong mixing coefficient of ARCH sequence. Second is the bound for maximum of residual empirical process in the same model. We illustrate their usefulness by proving…

Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…

The harmonizable Piranashvili-type stochastic processes are approximated by finite time shifted average sampling sums. Explicit truncation error upper bounds are established. Various corollaries and special cases are discussed.

(This is the third version of a working paper.) We develop a family of self-normalized concentration inequalities for marginal mean under martingale-difference structure and $\phi/\tilde{\phi}$-mixing conditions, where the latter includes…

We establish Hoeffding-type concentration inequalities for the low and high tail bounds of sums of exchangeable random variables. Our results exhibit an anti-symmetry in such tail bounds due to the assumption of exchangeability, a…

The theory of rapid mixing random walks plays a fundamental role in the study of modern randomised algorithms. Usually, the mixing time is measured with respect to the worst initial position. It is well known that the presence of…

We study the mixing time of the unit-rate zero-range process on the complete graph, in the regime where the number $n$ of sites tends to infinity while the density of particles per site stabilizes to some limit $\rho>0$. We prove that the…

This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…

Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…

This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…

We prove explicit finite-$N$ lower bounds for $\mathbb P(\bigcup_{k=1}^N A_k)$ when the $\sigma$-algebras generated by an event sequence satisfy quantitative $\varphi$- or $\alpha$-mixing bounds. The main $\varphi$-mixing estimate is…

In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types, the resulting measurements thus give only…

We study Markov processes on weighted directed hypergraphs where the state of at most one vertex can change at a time. Our setting is general enough to include simplicial epidemic processes, processes on multilayered networks or even the…

This article uses a combination of three ideas from simulation to establish a nearly optimal polynomial upper bound for the joint density of the stable process and its associated supremum at a fixed time on the entire support of the joint…