I. Simonelli

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20182023

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math.PR2023

A central limit theorem for a card shuffling problem

Shane Chern, Lin Jiu, Italo Simonelli

Given a positive integer $n$ , consider a random permutation $τ$ of the set ${1, 2, \dots, n}$ . In $τ$ , we look for sequences of consecutive integers that appear in adjacent positi…

math.PR2018

Local Limit Theorems for Poisson's Binomial in the Case of Infinite Expectation

Italo Simonelli, Lucia D. Simonelli

Let $V_{n} = X_{1, n} + X_{2, n} + \dots + X_{n, n}$ where $X_{i, n}$ are Bernoulli random variables which take the value $1$ with probability $b (i; n)$ . Let $λ_{n} = \sum\limits_{i=1…