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Probabilistic interpretations of Bernoulli, Stirling and Eulerian numbers

Friday, January 31, 2020 - 2:00pm
"Probabilistic interpretations of Bernoulli, Stirling and Eulerian numbers"

It is known that the Bernoulli, Stirling and Eulerian numbers are involved in the description of the probability functions, moments and cumulants of various classical probability distributions. These include the binomial, Poisson, geometric and negative binomial, the distribution of a sum of independent uniform variables, both discrete and continuous, and some distributions related to Brownian motion and the Riemann zeta function. I will review some of these relations, which involve a number Persi's favorite topics: excursions of random walks, Fourier analysis, random partitions, cycles and descents of permutations, and stationary one-dependent sequences.