1) La descarga del recurso depende de la página de origen
2) Para poder descargar el recurso, es necesario ser usuario registrado en Universia


Opción 1: Descargar recurso

Opción 2: Descargar recurso

Detalles del recurso

Descripción

We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation $\pi\in\mathbb{S}_{n}$ is proportional to $q^{\operatorname{inv}(\pi)}$ where $q>0$ and $\operatorname{inv}(\pi)$ is the number of inversions in $\pi$. ¶ We focus on the case that $q<1$ and show that the expected length of the cycle containing a given point is of order $\min\{(1-q)^{-2},n\}$. This marks the existence of two asymptotic regimes: with high probability, when $n$ tends to infinity with $(1-q)^{-2}\ll n$ then all cycles have size $o(n)$ whereas when $n$ tends to infinity with $(1-q)^{-2}\gg n$ then macroscopic cycles, of size proportional to $n$, emerge. In the second regime, we prove that the distribution of normalized cycle lengths follows the Poisson–Dirichlet law, as in a uniformly random permutation. The results bear formal similarity with a conjectured localization transition for random band matrices. ¶ Further results are presented for the variance of the cycle lengths, the expected diameter of cycles and the expected number of cycles. The proofs rely on the exact sampling algorithm for the Mallows distribution and make use of a special diagonal exposure process for the graph of the permutation.

Pertenece a

Project Euclid (Hosted at Cornell University Library)  

Autor(es)

Gladkich, Alexey -  Peled, Ron - 

Id.: 71074666

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveMallows permutations - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 Institute of Mathematical Statistics

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0091-1798
[References] 2168-894X

Fecha de contribución: 10-mar-2018

Contacto:

Localización:
* doi:10.1214/17-AOP1202

Otros recursos del mismo autor(es)

  1. Rigidity of 3-colorings of the discrete torus We prove that a uniformly chosen proper $3$-coloring of the $d$-dimensional discrete torus has a ver...
  2. Exponential decay of loop lengths in the loop $O(n)$ model with large $n$ International audience

Otros recursos de la mismacolección

  1. Errata to “Distance covariance in metric spaces” We correct several statements and proofs in our paper, Ann. Probab. 41, no. 5 (2013), 3284–3305.
  2. On the mixing time of Kac’s walk and other high-dimensional Gibbs samplers with constraints Determining the total variation mixing time of Kac’s random walk on the special orthogonal group $\m...
  3. Stochastic Airy semigroup through tridiagonal matrices We determine the operator limit for large powers of random symmetric tridiagonal matrices as the siz...
  4. On the spectral radius of a random matrix: An upper bound without fourth moment Consider a square matrix with independent and identically distributed entries of zero mean and unit ...
  5. Weak symmetric integrals with respect to the fractional Brownian motion The aim of this paper is to establish the weak convergence, in the topology of the Skorohod space, o...

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.