Related papers: Second Order Asymptotics for Random Number Generat…
This paper studies the second-order asymptotics of the discrete memoryless multiple-access channel with degraded message sets. For a fixed average error probability $\epsilon\in(0,1)$ and an arbitrary point on the boundary of the capacity…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
Let (X_n,Y_n), n\ge 1 be bivariate random claim sizes with common distribution function F and let N(t), t \ge 0 be a stochastic process which counts the number of claims that occur in the time interval [0,t], t\ge 0. In this paper we derive…
A generalized multisensor sequential change detection problem is considered, in which a number of (possibly correlated) sensors monitor an environment in real time, the joint distribution of their observations is determined by a global…
The article explores the asymptotic behavior of the expected number of drawings in the Coupon Collector's Problem with group-drawing under the uniform distribution. In this variant, each draw consists of a package of $s$ distinct coupons…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
We consider the Random Euclidean Assignment Problem in dimension $d=1$, with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings…
A general method to produce uniformly distributed pseudorandom numbers with extended precision by combining two pseudorandom numbers with lower precision is proposed. In particular, this method can be used for pseudorandom number generation…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…
We study semiorders induced by points drawn from a uniform random distribution. Of particular interest in this paper are the probabilities of generating specific semiorders and the equivalence classes they produce. We present a method for…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
We produce two strings of quantum random numbers simultaneously from the intensity fluctuations of the twin beams generated by a nondegenerate optical parametric oscillator. Two strings of quantum random numbers with bit rates up to 60 Mb/s…
An asymptotic series in Ramanujan's second notebook (Entry 10, Chapter 3) is concerned with the behavior of the expected value of $\phi(X)$ for large $\lambda$ where $X$ is a Poisson random variable with mean $\lambda$ and $\phi$ is a…
We consider two related problems arising from a question of R. Graham on quasirandom phenomena in permutation patterns. A ``pattern'' in a permutation $\sigma$ is the order type of the restriction of $\sigma : [n] \to [n]$ to a subset $S…
This paper studies the joint data and semantics lossy compression problem, i.e., an extension of the hidden lossy source coding problem that entails recovering both the hidden and observable sources. We aim to study the nonasymptotic and…