We prove the following conjecture, due to Tomaszewski (1986): Let X=∑ i= 1 naixi, where∑
iai 2= 1 and each xi is a uniformly random sign. Then Pr⁡[| X|≤ 1]≥ 1/2. Our main novel …

In this short note, we prove an asymptotic expansion for the ratio of the Dirichlet density to
the multivariate normal density with the same mean and covariance matrix. The expansion is …

We introduce a new version of Stein's method of comparison of operators specifically
tailored to the problem of bounding the L 1 (aka Wasserstein-1) distance between …

We introduce a version of Stein's method of comparison of operators specifically tailored to
the problem of bounding the Wasserstein-1 distance between continuous and discrete …

In this short note, we develop a local approximation for the log-ratio of the multivariate
hypergeometric probability mass function over the corresponding multinomial probability …

We prove a law of the iterated logarithm (LIL) for an infinite sum of independent indicators
parameterized by t and monotone in t as t→∞. It is shown that if the expectation b and the …

The aim of this paper is to present a new proof of an explicit version of the Berry--Esseen
type inequality of Bolthausen [Z. Wahrsch. Verw. Gebiete, 66 (1984), pp. 379--386]. The …

This thesis explores local and global normal and Edgeworth approximations for symmetric
binomial distributions. Further, it examines the normal approximation of convolution powers …

Narayana numbers appear in many places in combinatorics and probability, and it is known
that they are asymptotically normal. Using Stein's method of exchangeable pairs, we provide …

We prove Tomaszewski's conjecture (1986): Let f:{− 1, 1} n→ ℝ be of the form f (x)=∑ i= 1
naixi. Then Pr [| f (x)|≤√ Var [f]]≥ 1/2. Our main novel tools are local concentration …