Benjamini, Itai
Overview
Works:  21 works in 57 publications in 3 languages and 934 library holdings 

Roles:  Author, Editor, 958, Opponent, 956 
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
)
17 editions published in 2013 in English and held by 96 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)
17 editions published in 2013 in English and held by 96 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
)
7 editions published in 2011 in English and held by 46 WorldCat member libraries worldwide
This volume is dedicated to the memory of the late Oded Schramm (19612008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström 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 Sensitivity, Random Walks and Graph Limits, Percolation, and finally SchrammLoewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects
7 editions published in 2011 in English and held by 46 WorldCat member libraries worldwide
This volume is dedicated to the memory of the late Oded Schramm (19612008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström 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 Sensitivity, Random Walks and Graph Limits, Percolation, and finally SchrammLoewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects
Selected works of Oded Schramm by
Itai Benjamini(
)
2 editions published in 2011 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 2011 in English and held by 9 WorldCat member libraries worldwide
Selected works by
Oded Schramm(
)
1 edition published in 2011 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 8 WorldCat member libraries worldwide
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
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
Martin capacity for Markov chains and random walks in varying dimensions by
Itai Benjamini(
Book
)
2 editions published between 1993 and 1994 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1993 and 1994 in English and held by 3 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
On the effect of adding $ \epsilon $ Bernoulli percolation to everywhere percolating subgraphs of $ Z^ d $ 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
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
Planarité et Localité en Percolation by
Vincent Tassion(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
Cette thèse s'inscrit dans l'étude mathématique de la percolation, qui regroupe une famille de modèles présentant une transition de phase. Des avancées majeures au cours des quinze dernières années, notamment l'invention du SLE et la preuve de l'invariance conforme de la percolation de Bernoulli critique, nous permettent aujourd'hui d'avoir une image très complète de la percolation de Bernoulli sur le réseau triangulaire. Cependant, de nombreuses questions demeurent ouvertes, et ont motivé notre travail.La première d'entre elle est l'universalité de la percolation plane, qui affirme que les propriétés macroscopiques de la percolation plane critique ne devraient pas dépendre du réseau sousjacent à sa définition. Nous montrons, dans le cadre de la percolation Divide and Color, un résultat qui va dans le sens de cette universalité et identifions, dans ce contexte, des phénomènes macroscopiques indépendants du réseau microscopique. Une version plus faible d'universalité est donnée par la théorie de RussoSeymourWelsh (RSW), et sa validité est connue pour la percolation de Bernoulli (sans dépendance) sur les réseaux plans suffisamment symétriques. Nous étudions de nouveaux arguments de type RSW pour des modèles de percolation avec dépendance. La deuxième question que nous avons abordée est celle de l'absence d'une composante connexe ouverte infinie au point critique, une question importante du point de vue physique, puisqu'elle traduit la continuité de la transition de phase. Dans deux travaux en collaboration avec Hugo DuminilCopin et Vladas Sidoravicius, nous montrons que la transition de phase est continue pour la percolation de Bernoulli sur le graphe Z^2x{0,...,k}, et pour la percolation FK sur le réseau carré avec paramètre q inférieur ou égal à 4. Enfin, la dernière question qui nous a guidés est la localité du point critique : la donnée des boules de grands rayons d'un graphe suffitelle à identifier avec une bonne précision la valeur du point critique? Dans un travail en collaboration avec Sébastien Martineau, nous répondons de manière affirmative à cette question dans le cadre des graphes de Cayley de groupes abéliens
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
Cette thèse s'inscrit dans l'étude mathématique de la percolation, qui regroupe une famille de modèles présentant une transition de phase. Des avancées majeures au cours des quinze dernières années, notamment l'invention du SLE et la preuve de l'invariance conforme de la percolation de Bernoulli critique, nous permettent aujourd'hui d'avoir une image très complète de la percolation de Bernoulli sur le réseau triangulaire. Cependant, de nombreuses questions demeurent ouvertes, et ont motivé notre travail.La première d'entre elle est l'universalité de la percolation plane, qui affirme que les propriétés macroscopiques de la percolation plane critique ne devraient pas dépendre du réseau sousjacent à sa définition. Nous montrons, dans le cadre de la percolation Divide and Color, un résultat qui va dans le sens de cette universalité et identifions, dans ce contexte, des phénomènes macroscopiques indépendants du réseau microscopique. Une version plus faible d'universalité est donnée par la théorie de RussoSeymourWelsh (RSW), et sa validité est connue pour la percolation de Bernoulli (sans dépendance) sur les réseaux plans suffisamment symétriques. Nous étudions de nouveaux arguments de type RSW pour des modèles de percolation avec dépendance. La deuxième question que nous avons abordée est celle de l'absence d'une composante connexe ouverte infinie au point critique, une question importante du point de vue physique, puisqu'elle traduit la continuité de la transition de phase. Dans deux travaux en collaboration avec Hugo DuminilCopin et Vladas Sidoravicius, nous montrons que la transition de phase est continue pour la percolation de Bernoulli sur le graphe Z^2x{0,...,k}, et pour la percolation FK sur le réseau carré avec paramètre q inférieur ou égal à 4. Enfin, la dernière question qui nous a guidés est la localité du point critique : la donnée des boules de grands rayons d'un graphe suffitelle à identifier avec une bonne précision la valeur du point critique? Dans un travail en collaboration avec Sébastien Martineau, nous répondons de manière affirmative à cette question dans le cadre des graphes de Cayley de groupes abéliens
Selected Works of Oded Schramm by
Itai Benjamini(
Book
)
5 editions published in 2011 in English and held by 1 WorldCat member library 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
5 editions published in 2011 in English and held by 1 WorldCat member library 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
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
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
This thesis deals with two kinds of statistical mechanics problems: percolation ongroups and directed models. In the first case, we realise the group under considerationas a geometric object (via the notion of Cayley graph) before breaking it apartrandomly. The study of this process reveals deep connections between the geometricproperties of a group and the behaviour of Bernoulli percolation on it. In the secondcase, we focus on models where up and down play different roles, which makes severalquestions less hard to tackle.Chapter 1 strengthens the Indistinguishability Theorem of LyonsSchramm, whichstates that the infinite clusters yielded by a Bernoulli percolation on a Cayley graphalmost surely all look alike. The nonTriviality of this strengthening is illustrated bya directed model that satisfies the Indistinguishability Property but not the StrongIndistinguishability Property.Chapter 2 has been obtained in collaboration with Vincent Tassion. We show thatthe value of the critical parameter for Bernoulli percolation essentially only dependson the local structure of the considered abelian Cayley graph.In Chapter 3, we introduce a directed version of the DLA model, for which weestablish the existence of an infinite volume dynamics, control the propagation ofinformation and prove asymptotic inequalities on the width and height of the cluster
1 edition published in 2014 in French and held by 1 WorldCat member library worldwide
This thesis deals with two kinds of statistical mechanics problems: percolation ongroups and directed models. In the first case, we realise the group under considerationas a geometric object (via the notion of Cayley graph) before breaking it apartrandomly. The study of this process reveals deep connections between the geometricproperties of a group and the behaviour of Bernoulli percolation on it. In the secondcase, we focus on models where up and down play different roles, which makes severalquestions less hard to tackle.Chapter 1 strengthens the Indistinguishability Theorem of LyonsSchramm, whichstates that the infinite clusters yielded by a Bernoulli percolation on a Cayley graphalmost surely all look alike. The nonTriviality of this strengthening is illustrated bya directed model that satisfies the Indistinguishability Property but not the StrongIndistinguishability Property.Chapter 2 has been obtained in collaboration with Vincent Tassion. We show thatthe value of the critical parameter for Bernoulli percolation essentially only dependson the local structure of the considered abelian Cayley graph.In Chapter 3, we introduce a directed version of the DLA model, for which weestablish the existence of an infinite volume dynamics, control the propagation ofinformation and prove asymptotic inequalities on the width and height of the cluster
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 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
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
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