Benjamini, Itai
Overview
Works:  19 works in 51 publications in 3 languages and 616 library holdings 

Roles:  Author, Editor, 958 
Classifications:  QA276, 519.5 
Publication Timeline
.
Most widely held works by
Itai Benjamini
Coarse geometry and randomness : École d'été de probabilités de SaintFlour XLI  2011 by
Itai Benjamini(
Book
)
14 editions published in 2013 in English and held by 88 WorldCat member libraries worldwide
These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ)
14 editions published in 2013 in English and held by 88 WorldCat member libraries worldwide
These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ)
Selected works of Oded Schramm by
Oded Schramm(
Book
)
14 editions published in 2011 in English and held by 55 WorldCat member libraries worldwide
This volume is dedicated to the memory of the late Oded Schramm (19612008), distinguished statistician. Throughout his life, Oded made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Haggstrom have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Haggstrom and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensiti
14 editions published in 2011 in English and held by 55 WorldCat member libraries worldwide
This volume is dedicated to the memory of the late Oded Schramm (19612008), distinguished statistician. Throughout his life, Oded made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Haggstrom have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Haggstrom and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensiti
Noise sensitivity of Boolean functions and applications to percolation by
Itai Benjamini(
Book
)
2 editions published in 1999 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 7 WorldCat member libraries worldwide
Selected works by
Oded Schramm(
)
1 edition published in 2011 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 7 WorldCat member libraries worldwide
Noise sensitivity of Boolean functions and applications to percolation. A 1homotopy theory of schemes / by Fabien Morel ;
Vladimir Voevodsky [u.a.] by
Itai Benjamini(
Book
)
1 edition published in 2001 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 5 WorldCat member libraries worldwide
On random graph homomorphisms into Z by
Itai Benjamini(
Book
)
2 editions published in 1999 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 2 WorldCat member libraries worldwide
Selected works of Oded Schramm by
Oded Schramm(
Book
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Martin capacity for Markov chains and random walks in varying dimensions by
Itai Benjamini(
Book
)
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
Selected works of Oded Schramm by
Oded Schramm(
Book
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
On the effect of adding eBernoulli percolation to everywhere percolating subgraphs of Z d by
Itai Benjamini(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Heat kernel bounds on Riemanian manifolds by
Itai Benjamini(
Book
)
2 editions published in 1993 in English and held by 1 WorldCat member library worldwide
2 editions published in 1993 in English and held by 1 WorldCat member library worldwide
Percolation of arbitrary words in (01) by
Itai Benjamini(
Book
)
2 editions published in 1993 in English and held by 1 WorldCat member library worldwide
2 editions published in 1993 in English and held by 1 WorldCat member library worldwide
Mixing times of the biased card shuffling and the asymmetric exclusion process by
Itai Benjamini(
)
1 edition published in 2005 in Undetermined and held by 1 WorldCat member library worldwide
Consider the following method of card shuffling. Start with a deck of N cards numbered 1 through N. Fix a parameter p between 0 and 1. In this model a "shuffle" consists of uniformly selecting a pair of adjacent cards and then flipping a coin that is heads with probability p. If the coin comes up heads, then we arrange the two cards so that the lowernumbered card comes before the highernumbered card. If the coin comes up tails, then we arrange the cards with the highernumbered card first. In this paper we prove that for all p ≠ 1/2, the mixing time of this card shuffling is O(N^2), as conjectured by Diaconis and Ram (2000). Our result is a rare case of an exact estimate for the convergence rate of the Metropolis algorithm. A novel feature of our proof is that the analysis of an infinite (asymmetric exclusion) process plays an essential role in bounding the mixing time of a finite process
1 edition published in 2005 in Undetermined and held by 1 WorldCat member library worldwide
Consider the following method of card shuffling. Start with a deck of N cards numbered 1 through N. Fix a parameter p between 0 and 1. In this model a "shuffle" consists of uniformly selecting a pair of adjacent cards and then flipping a coin that is heads with probability p. If the coin comes up heads, then we arrange the two cards so that the lowernumbered card comes before the highernumbered card. If the coin comes up tails, then we arrange the cards with the highernumbered card first. In this paper we prove that for all p ≠ 1/2, the mixing time of this card shuffling is O(N^2), as conjectured by Diaconis and Ram (2000). Our result is a rare case of an exact estimate for the convergence rate of the Metropolis algorithm. A novel feature of our proof is that the analysis of an infinite (asymmetric exclusion) process plays an essential role in bounding the mixing time of a finite process
Examples of simplyconnected Liouville manifolds with positive spectrum by
Itai Benjamini(
Book
)
2 editions published in 1993 in English and held by 1 WorldCat member library worldwide
2 editions published in 1993 in English and held by 1 WorldCat member library worldwide
Heat kernel lower bounds on Riemanian manifolds using the old ideas of Nash by
Itai Benjamini(
Book
)
2 editions published in 1993 in English and held by 1 WorldCat member library worldwide
2 editions published in 1993 in English and held by 1 WorldCat member library worldwide
Percolation sur les groupes et modèles dirigés by
Sébastien Martineau(
)
1 edition published in 2014 in French and held by 1 WorldCat member library worldwide
Cette thèse porte sur deux types de problèmes de mécanique statistique : il y est question de percolation sur les groupes et de modèles dirigés. Dans le premier cas,il s'agit de réaliser un groupe comme objet géométrique (via la notion de graphe de Cayley), puis de morceler ce dernier aléatoirement. L'étude de ce processus révèle des liens étroits entre les propriétés géométriques d'un groupe et le comportement de la percolation de Bernoulli sur celuiCi. Dans le second cas, on s'intéresse à des modèles où haut et bas jouent des rôles différents, ce qui permet de rendre un certain nombre de questions accessibles à l'étude rigoureuse.Le chapitre 1 renforce le théorème d'indistinguabilité de Lyons et Schramm en percolation, lequel stipule que les composantes connexes infinies fournies par la percolation de Bernoulli sur un graphe de Cayley ont presque sûrement toutes la même allure. La nonTrivialité de ce renforcement est illustrée par un modèle dirigé qui vérifie la propriété d'indistinguabilité mais pas la propriété renforcée.Le chapitre 2 est le fruit d'un travail réalisé en collaboration avec Vincent Tassion.On y démontre que la valeur du paramètre critique pour la percolation de Bernoulli ne dépend essentiellement que de la structure locale du graphe de Cayley abélien considéré.Dans le chapitre 3, on introduit une version dirigée du modèle DLA, pour laquelle on établit l'existence d'une dynamique en volume infini, un contrôle sur la propagation d'information et des inégalités asymptotiques sur la largeur et la hauteur de l'agrégat
1 edition published in 2014 in French and held by 1 WorldCat member library worldwide
Cette thèse porte sur deux types de problèmes de mécanique statistique : il y est question de percolation sur les groupes et de modèles dirigés. Dans le premier cas,il s'agit de réaliser un groupe comme objet géométrique (via la notion de graphe de Cayley), puis de morceler ce dernier aléatoirement. L'étude de ce processus révèle des liens étroits entre les propriétés géométriques d'un groupe et le comportement de la percolation de Bernoulli sur celuiCi. Dans le second cas, on s'intéresse à des modèles où haut et bas jouent des rôles différents, ce qui permet de rendre un certain nombre de questions accessibles à l'étude rigoureuse.Le chapitre 1 renforce le théorème d'indistinguabilité de Lyons et Schramm en percolation, lequel stipule que les composantes connexes infinies fournies par la percolation de Bernoulli sur un graphe de Cayley ont presque sûrement toutes la même allure. La nonTrivialité de ce renforcement est illustrée par un modèle dirigé qui vérifie la propriété d'indistinguabilité mais pas la propriété renforcée.Le chapitre 2 est le fruit d'un travail réalisé en collaboration avec Vincent Tassion.On y démontre que la valeur du paramètre critique pour la percolation de Bernoulli ne dépend essentiellement que de la structure locale du graphe de Cayley abélien considéré.Dans le chapitre 3, on introduit une version dirigée du modèle DLA, pour laquelle on établit l'existence d'une dynamique en volume infini, un contrôle sur la propagation d'information et des inégalités asymptotiques sur la largeur et la hauteur de l'agrégat
Selected Works of Oded Schramm, Volume 1(
)
1 edition published in 2011 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 0 WorldCat member libraries worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Useful Links