Related papers: Optimal Chernoff and Hoeffding Bounds for Finite S…

A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars,…

We provide finite sample upper and lower bounds on the Binomial tail probability which are a direct application of Sanov's theorem. We then use these to obtain high probability upper and lower bounds on the minimum of i.i.d. Binomial random…

This paper introduces a distribution-dependent PAC-Chernoff bound that exhibits perfect tightness for interpolators, even within over-parameterized model classes. This bound, which relies on basic principles of Large Deviation Theory,…

We prove a new bound to the exponential sum of the form $$ \sum_{h \sim H}\delta_h \mathop{\sum_{m\sim M}\sum_{n\sim N}}_{mn\sim x}a_{m}b_{n}\e\big(\alpha mn + h(mn + u)^{\gamma}\big), $$ by a new approach to the Type I sum. The sum can be…

We obtain some optimal inequalities on tail probabilities for sums of independent bounded random variables. Our main result completes an upper bound on tail probabilities due to Talagrand by giving a one-term asymptotic expansion for large…

We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002…

The paper studies the higher-order absolute differences taken from progressive terms of time-homogenous binary Markov chains. Two theorems presented are the limiting theorems for these differences, when their order $k$ converges to…

This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_d f(V), where f(v) = Av + g(v) for a random function g(v) = o(v) a.s. as v tends to infinity. Specifically, we provide…

The Markov, Chebyshev, and Chernoff inequalities are some of the most widely used methods for bounding the tail probabilities of random variables. In all three cases, the bounds are tight in the sense that there exists easy examples where…

We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…

In this paper, we treat an asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state and the completely mixed state by one-way LOCC, two-way LOCC, and…

Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite…

The aim of this paper is to develop a general theory for the class of skip-free Markov chains on denumerable state space. This encompasses their potential theory via an explicit characterization of their potential kernel expressed in terms…

Consider a sequence $P_n$ of positive recurrent transition matrices or kernels that approximate a limiting infinite state matrix or kernel $P_{\infty}$. Such approximations arise naturally when one truncates an infinite state Markov chain…

We study the quenched invariance principle for random conductance models with long range jumps on $\Z^d$, where the transition probability from $x$ to $y$ is, on average, comparable to $|x-y|^{-(d+\alpha)}$ with $\alpha\in (0,2)$ but is…

We derive a Fuk-Nagaev inequality for the maxima of norms of martingale sequences in smooth Banach spaces which allow for a finite number of higher conditional moments. The bound is obtained by combining an optimization approach for a…

We consider a bivariate Markov chain $Z=\{Z_k\}_{k \geq 1}=\{(X_k,Y_k)\}_{k \geq 1}$ taking values on product space ${\cal Z}={\cal X} \times{ \cal Y}$, where ${\cal X}$ is possibly uncountable space and ${\cal Y}=\{1,\ldots, |{\cal Y}|\}$…

We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising model at criticality, independent of the boundary conditions. Our proof relies mainly on Smirnov's fermionic observable for the FK Ising model,…

Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname…

We prove central limit theorems, Berry-Esseen type theorems, almost sure invariance principles, large deviations and Livsic type regularity for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j(...,X_{j-1},X_j,X_{j+1},...)$, where $(X_j)$…