Related papers: Upper and lower bounds for the correlation functio…

We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…

We present a new and simple approach to concentration inequalities for functions around their expectation with respect to non-product measures, i.e., for dependent random variables. Our method is based on coupling ideas and does not use…

We consider a general class of spin systems with potentially unbounded real-valued spins, defined via a single-site potential with super-Gaussian tails on general graphs, allowing for both short- and long-range interactions. This class…

The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in…

We compute the whole asymptotic expansion of the probability that a large uniform labeled graph is connected, and of the probability that a large uniform labeled tournament is irreducible. In both cases, we provide a combinatorial…

We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our technique is based on inducing the non-uniformly expanding system to a uniformly expanding one, and on showing…

We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical…

In this article we show that a large class of infinite measure preserving dynamical systems that do not admit physical measures nevertheless exhibit strong statistical properties. In particular, we give sufficient conditions for existence…

In this article we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We deal with two classes of such systems: attracting and parabolic. The latter being…

We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function…

We develop a renormalization theory of non-perturbative dissipative H\'enon-like maps with combinatorics of bounded type. The main novelty of our approach is the incorporation of Pesin theoretic ideas to the renormalization method, which…

We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…

Although inverse limits with factor spaces indexed by the positive integers are most commonly studied, Ingram and Mahavier have defined inverse limits with set-valued functions broadly enough for any directed index set to be used. In this…

Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…

The filtering problem for finite state Markov chains is revisited, when the intensity of the observation noise increases. We give a description of conditional measure concentration around the invariant distribution of the signal and derive…

We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit…

We construct an invariant measure for a piecewise analytic interval map whose Lyapunov exponent is not defined. Moreover, for a set of full measure, the pointwise Lyapunov exponent is not defined. This map has a Lorenz-like singularity and…

We study probabilistic iterated function systems (IFS), consisting of a finite or infinite number of average-contracting bi-Lipschitz maps on R^d. If our strong open set condition is also satisfied, we show that both upper and lower bounds…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov…