F. Kochman

activity

20132016

most citedExtensions of Billingsley's Theorem via Multi-Intensities

3 citations · 5 across the 4 of their papers we have counts for

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math.PR2016

Large deviation asymptotics for a random variable with Lévy measure supported by $[0, 1]$

Richard Arratia, Fred Kochman, Sandy Zabell

Asymptotics for Dickman's number theoretic function $ρ (u)$ , as $u \to \infty$ , were given de Bruijn and Alladi, and later in sharper form by Hildebrand and Tenenbaum. The p…

math.PR2014

Poisson--Dirichlet Limit Theorems in Combinatorial Applications via Multi-Intensities

Richard Arratia, Fred Kochman

We present new, exceptionally efficient proofs of Poisson--Dirichlet limit theorems for the scaled sizes of irreducible components of random elements in the classic combinatorial c…

math.PR2014★ 3 cited

Extensions of Billingsley's Theorem via Multi-Intensities

Richard Arratia, Fred Kochman, Victor S. Miller

Let $p_{1} \geq p_{2} \geq \dots$ be the prime factors of a random integer chosen uniformly from $1$ to $n$ , and let $\frac{lo g p _{1}}{lo g n}, \frac{lo g p _{2}}{lo g n}, \dots$ be the…

math.PR2014★ 2 cited

A Simple Direct Proof of Billingsley's Theorem

Richard Arratia, Fred Kochman

Billingsley's theorem (1972) asserts that the Poisson--Dirichlet process is the limit, as $n \to \infty$ , of the process giving the relative log sizes of the largest prime factor,…

math.PR2013

Size bias for one and all

Richard Arratia, Larry Goldstein, Fred Kochman

Size bias occurs famously in waiting-time paradoxes, undesirably in sampling schemes, and unexpectedly in connection with Stein's method, tightness, analysis of the lognormal distr…