5 citations · 6 across the 4 of their papers we have counts for
4 papers · 1 filter
A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three
Jungeun Park, Douglas Rizzolo
We use local limits of Galton-Watson trees to establish local limit theorems for permutations conditioned to avoid a pattern of length three. In the case of 321-avoiding permutatio…
The Aldous diffusion: a stationary evolution of the Brownian CRT
Noah Forman, Soumik Pal, Douglas Rizzolo +1
Motivated by a down-up Markov chain on cladograms, David Aldous conjectured in 1999 that there exists a "diffusion on continuum trees" whose mass partitions at any finite number of…
Diffusions on a space of interval partitions with Poisson-Dirichlet stationary distributions
Noah Forman, Soumik Pal, Douglas Rizzolo +1
We construct a pair of related diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters (1/2,0)…
Pattern-avoiding permutations and Brownian excursion Part I: Shapes and fluctuations
Christopher Hoffman, Douglas Rizzolo, Erik Slivken
Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology…