Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Rizzolo, Douglas"'
Autor:
Park, Jungeun, Rizzolo, Douglas
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 permutations our results resolve an open problem of Pinsky. In the other cases o
Externí odkaz:
http://arxiv.org/abs/2401.01957
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 branch points evolve as Wright-Fisher diffusions with some negative m
Externí odkaz:
http://arxiv.org/abs/2305.17269
We prove that the critical value of the one-dimensional Stochastic Sandpile Model is less than one. This verifies a conjecture of Rolla and Sidoravicius.
Comment: 44 pages
Comment: 44 pages
Externí odkaz:
http://arxiv.org/abs/2212.08293
Autor:
Rivera-Lopez, Kelvin, Rizzolo, Douglas
We obtain a concentration inequality for the maximum degree of a vertex in a uniformly random dissection of a polygon. This resolves a conjecture posed by Curien and Kortchemski in 2012. Our approach is based on a bijection with dual trees and the to
Externí odkaz:
http://arxiv.org/abs/2204.01687
Autor:
Rivera-Lopez, Kelvin, Rizzolo, Douglas
Recently there has been significant interest in constructing ordered analogues of Petrov's two-parameter extension of Ethier and Kurtz's infinitely-many-neutral-alleles diffusion model. One method for constructing these processes goes through taking
Externí odkaz:
http://arxiv.org/abs/2110.10848
In previous work, we constructed Fleming--Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval $[0,1]$) that are stationary with the Poisson--Dirichlet laws with parameters $\alpha\in(0,1)$ and $\
Externí odkaz:
http://arxiv.org/abs/2101.09307
Autor:
Rivera-Lopez, Kelvin, Rizzolo, Douglas
We construct a two-parameter family of Feller diffusions on the set of open subsets of $(0,1)$ that arise as diffusive limits of two-parameter ordered Chinese Restaurant Process up-down chains. The diffusions we construct are natural ordered analogue
Externí odkaz:
http://arxiv.org/abs/2011.06577
We introduce and study interval partition diffusions with Poisson--Dirichlet$(\alpha,\theta)$ stationary distribution for parameters $\alpha\in(0,1)$ and $\theta\ge 0$. This extends previous work on the cases $(\alpha,0)$ and $(\alpha,\alpha)$ and bu
Externí odkaz:
http://arxiv.org/abs/2008.02823
Publikováno v:
Ann. Appl. Probab. 32 (3) 2211 - 2253, 2022
We give a pathwise construction of a two-parameter family of purely-atomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson-Dirichlet$(\alpha,\theta)$ distributions, for $\alpha\in (0,1)$ and $\theta\ge 0$. Th
Externí odkaz:
http://arxiv.org/abs/2007.05250
We determine the scaling limit for permutations conditioned to have longest decreasing subsequence of length at most $d$. These permutations are also said to avoid the pattern $(d+1)d \cdots 2 1$ and they can be written as a union of $d$ increasing s
Externí odkaz:
http://arxiv.org/abs/1911.04982