Colloquium Speaker:
Dr. Éric Marchand, Ph.D.
Université de Sherbrooke, Quebec
Title: From the distribution of string counts in Bernoulli sequences to multivariate discrete models
Abstract: I will provide a personalized account of a sequence of problems, that I have worked on over the years, beginning with string counts in Bernoulli sequences and transiting to multivariate discrete models. As a starting point, we consider independent Bernoulli trials with varying success probabilities 1/k for the kth trial, the sum of the products of two consecutive occurrences, and the problem of establishing that the sum is distributed Poisson with mean equal to 1. We will explain how this finding connects to cycles in random permutations, records for continuous random variables, the Hoppe-Polya urn, and the classical Montmort matching problem. Extensions to other success probabilities will be discussed and we present a multivariate version with Bernoulli arrays having multinomial independently distributed rows, where the object of the study is the joint distribution of column totals. For a certain configuration of the underlying parameters, a multivariate Poisson mixture with Dirichlet mixing arises and relates to multivariate discrete models with common margins, as well as to a sum and shares model developed with Chris Jones, to a multivariate splitting model by Peyhardi et al. (2021), and to a tree Polya splitting model by Valiquette et al. (2025).
Day & Time: Thursday, April 2, 2026, at 3:00pm
Location: Lambton Tower, Room 9-118
Counts toward seminar attendance for MSc and PhD students in Math & Stats.