Related papers: Probability asymptotics: notes on notation
There are many randomness notions. On the classical account, many of them are about whether a given infinite binary sequence is random for some given probability. If so, this probability turns out to be the same for all these notions, so…
In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…
We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.
We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the…
A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random…
In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new…
In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl. Probab. 2021] we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and…
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…
A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique"…
This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants. They may be indicative of some deep phenomena in symplectic topology that in full generality are outside…
The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
We consider a one-dimensional random walk $S_n$ having i.i.d. increments with zero mean and finite variance. We continue our study of asymptotic expansions for local probabilities $\mathbf P(S_n=x,\tau_0>n)$, which has been started in…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
The paper considers asymptotics of summation functions of additive and multiplicative arithmetic functions. We also study asymptotics of summation functions of natural and prime arguments. Several assertions on this subject are proved and…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…
We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.