相关论文: Nearly tight universal bounds for the binomial tai…
Estimating the parameters from $k$ independent Bin$(n,p)$ random variables, when both parameters $n$ and $p$ are unknown, is relevant to a variety of applications. It is particularly difficult if $n$ is large and $p$ is small. Over the past…
New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…
We establish new Bonferroni-type lower bounds for the probability of a union of finitely many events where the selection of intersections in the estimates is determined by the clique complex of a chordal graph.
In this paper, we prove exponential tail bounds for canonical (or degenerate) $U$-statistics and $U$-processes under exponential-type tail assumptions on the kernels. Most of the existing results in the relevant literature often assume…
We obtain explicit bounds on the truncation error of the cumulant series of a bounded complex function of a random vector with independent components. The bounds are based on multidimensional differences. This extends the theory of the…
We show how to find upper and lower bounds to the median of a gamma distribution, over the entire range of shape parameter $k > 0$, that are the tightest possible bounds of the form $2^{-1/k} (A + Bk)$, with closed-form parameters $A$ and…
We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…
Recently, a new set of positivity bounds with $t$ derivatives have been discovered. We explore the generic features of these generalized positivity bounds with loop amplitudes and apply these bounds to constrain the parameters in chiral…
In this paper we study the redundancy of Huffman codes. In particular, we consider sources for which the probability of one of the source symbols is known. We prove a conjecture of Ye and Yeung regarding the upper bound on the redundancy of…
We consider a supercritical Galton-Watson process $Z_n$ whose offspring distribution has mean $m>1$ and is bounded by some $d\in \{2,3,\ldots\}$. As well-known, the associated martingale $W_n=Z_n/m^n$ converges a.s. to some nonnegative…
In this paper I prove a conjecture which gives a lower bound for the largest absolute value of the coefficients of the n-th cyclotomic polynomial for some n. Moreover this estimate is essentially sharp.
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…
In our recent research endeavors, we have delved into the realm of tail bounds problems concerning bivariate random tensor means. In this context, tensors are treated as finite-dimensional operators. However, the longstanding challenge of…
For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…
The upper tail problem in the Erd\H{o}s--R\'enyi random graph $G\sim\mathcal{G}_{n,p}$ asks to estimate the probability that the number of copies of a graph $H$ in $G$ exceeds its expectation by a factor $1+\delta$. Chatterjee and Dembo…
Probabilistic recurrence relations (PRRs) are a standard formalism for describing the runtime of a randomized algorithm. Given a PRR and a time limit $\kappa$, we consider the classical concept of tail probability $\Pr[T \ge \kappa]$, i.e.,…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In…
In high dimensional percolation at parameter $p < p_c$, the one-arm probability $\pi_p(n)$ is known to decay exponentially on scale $(p_c - p)^{-1/2}$. We show the same statement for the ratio $\pi_p(n) / \pi_{p_c}(n)$, establishing a form…
In this paper, we investigate the question: Given a small number of datapoints, for example N = 30, how tight can PAC-Bayes and test set bounds be made? For such small datasets, test set bounds adversely affect generalisation performance by…