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J. Jonasson (2008)
Dynamical circle covering with homogeneous Poisson updatingStatistics & Probability Letters, 78
P. Nolin (2007)
Near-critical percolation in two dimensionsElectronic Journal of Probability, 13
J. Kahn, G. Kalai, N. Linial (1988)
The influence of variables on Boolean functions[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
T. Hara, G. Slade (1994)
Mean-Field Behaviour and the Lace Expansion
D. Aldous, J. Propp (1998)
Microsurveys in Discrete ProbabilityJournal of the American Statistical Association, 41
O. Adelman, K. Burdzy, Robin Pemantle (1997)
SETS AVOIDED BY BROWNIAN MOTIONAnnals of Probability, 26
R. O'Donnell, M. Sudan (2003)
Computational applications of noise sensitivity
F. Camia, L. Fontes, C. Newman (2006)
Two-dimensional scaling limits via marked nonsimple loopsBulletin of the Brazilian Mathematical Society, 37
D. Khoshnevisan (2002)
Multiparameter Processes: An Introduction to Random Fields
G. Kalai, S. Safra (2006)
Threshold Phenomena and Influence: Perspectives from Mathematics, Computer Science, and Economics
Erik Broman, J. Steif (2006)
Dynamical Stability of Percolation for Some Interacting Particle Systems and $\epsilon$--StabilityAnnals of Probability, 34
(2008)
Probability on Trees and Networks In preparation. Current version available at http://mypage
M. Aizenman, H. Kesten, C. Newman (1987)
Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolationCommunications in Mathematical Physics, 111
I. Benjamini, O. Schramm (1998)
Exceptional planes of percolationProbability Theory and Related Fields, 111
H. Kesten (1986)
Subdiffusive behavior of random walk on a random clusterAnnales De L Institut Henri Poincare-probabilites Et Statistiques, 22
H. Kesten (1986)
The incipient infinite cluster in two-dimensional percolationProbability Theory and Related Fields, 73
G. Lawler (2007)
Dimension and natural parametrization for SLE curvesarXiv: Probability
Pete explaining to me their unpublished work. A part of this work was done while visiting the Mittag-Leffler Institute in Djursholm, Sweden, the same institute where dynamical percolation was started
S. Smirnov (2001)
Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limitsComptes Rendus De L Academie Des Sciences Serie I-mathematique, 333
Y. Peres (1996)
Remarks on intersection-equivalence and capacity-equivalenceAnnales De L Institut Henri Poincare-physique Theorique, 64
Y. Peres, O. Schramm, S. Sheffield, D. Wilson (2005)
Random-Turn Hex and Other Selection GamesThe American Mathematical Monthly, 114
Elchanan Mossel, R. O'Donnell (2003)
On the noise sensitivity of monotone functionsRandom Structures & Algorithms, 23
G. Lawler, O. Schramm, W. Werner (2001)
One-Arm Exponent for Critical 2D PercolationElectronic Journal of Probability, 7
T. Harris (1960)
A lower bound for the critical probability in a certain percolation processMathematical Proceedings of the Cambridge Philosophical Society, 56
BY Erik, I., Broman, Jeffrey, É., Steif (2004)
DYNAMICAL STABILITY OF PERCOLATION FOR SOME INTERACTING PARTICLE SYSTEMS AND ε -MOVABILITY
Steif Mathematical Sciences Chalmers University of Technology and Mathematical Sciences Göteborg University SE-41296 Gothenburg, Sweden e-mail: steif@chalmers
A. Percus, Gabriel Istrate, C. Moore (2006)
Computational Complexity and Statistical Physics
O. Schramm, J. Steif (2005)
Quantitative noise sensitivity and exceptional times for percolationAnnals of Mathematics, 171
C. Garban (2010)
Oded Schramm's contributions to noise sensitivity.Annals of Probability, 39
Y. Peres (1996)
Intersection-equivalence of Brownian paths and certain branching processesCommunications in Mathematical Physics, 177
Local time for exceptional dynamical percolation, and the incipient infinite cluster
J. Doob (1953)
Stochastic processes
R. Langlands, P. Pouliot, Y. Saint-Aubin (1994)
Conformal invariance in two-dimensional percolationBulletin of the American Mathematical Society, 30
Y. Peres, J. Steif (1998)
The number of infinite clusters in dynamical percolationProbability Theory and Related Fields, 111
R. Lyons (1992)
Random Walks, Capacity and Percolation on TreesAnnals of Probability, 20
H. Kesten (1987)
Scaling relations for 2D-percolationCommunications in Mathematical Physics, 109
Russell Lyons and Gábor Pete for very many helpful comments on earlier versions of the manuscript. I appreciate in particular Christophe Garban, A survey on dynamical percolation 31
I. Benjamini, G. Kalai, O. Schramm (1998)
Noise sensitivity of Boolean functions and applications to percolationPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 90
F. Camia, C. Newman (2006)
Two-Dimensional Critical Percolation: The Full Scaling LimitCommunications in Mathematical Physics, 268
D. Khoshnevisan, Y. Peres, Yimin Xiao (2000)
Limsup Random FractalsElectronic Journal of Probability, 5
H. Kesten, Yu Zhang (1987)
Strict inequalities for some critical exponents in two-dimensional percolationJournal of Statistical Physics, 46
J. Berg, R. Meester, D. White (1997)
Dynamic Boolean modelsJournal of Fluid Mechanics
(1997)
Probab. et Stat
W. Werner (2007)
Lectures on two-dimensional critical percolationarXiv: Probability
S. Evans (1989)
Local properties of Lévy processes on a totally disconnected groupJournal of Theoretical Probability, 2
R. Burton, M. Keane (1989)
Density and uniqueness in percolationCommunications in Mathematical Physics, 121
Y. Peres, O. Schramm, J. Steif (2007)
Dynamical sensitivity of the infinite cluster in critical percolationAnnales De L Institut Henri Poincare-probabilites Et Statistiques, 45
I. Benjamini, Olle Häggström, Y. Peres, J. Steif (2003)
Which properties of a random sequence are dynamically sensitiveAnnals of Probability, 31
O. Schramm (1999)
Scaling limits of loop-erased random walks and uniform spanning treesIsrael Journal of Mathematics, 118
R. Lyons (1990)
Random Walks and Percolation on TreesAnnals of Probability, 18
Olle Häggström (1997)
Dynamical percolation: Early results and open problems
Yuval Peresy, Je Steifz (1996)
Dynamical Percolation
(2002)
Foundations of modern probability. Second edition. Probability and its Applications (New York)
D. Khoshnevisan (2007)
Dynamical percolation on general treesProbability Theory and Related Fields, 140
J. Cardy (1991)
Critical percolation in finite geometriesJournal of Physics A, 25
C. Garban, G. Pete, O. Schramm (2008)
The Fourier spectrum of critical percolationActa Mathematica, 205
H. Kesten (1980)
The critical probability of bond percolation on the square lattice equals 1/2Communications in Mathematical Physics, 74
S. Smirnov, W. Werner (2001)
CRITICAL EXPONENTS FOR TWO-DIMENSIONAL PERCOLATIONMathematical Research Letters, 8
Olle Häggström, Robin Pemantle (1999)
On near-critical and dynamical percolation in the tree caseRandom Struct. Algorithms, 15
G. Kalai, S. Safra, Feldman Building
בירושלים העברית האוניברסיטה the Hebrew University of Jerusalem Threshold Phenomena and Influence with Some Perspectives from Mathematics, Computer Science, and Economics הרציונליות לחקר מרכז Center for the Study of Rationality Threshold Phenomena and Influence with Some Perspectives from
J. Jonasson, J. Steif (2006)
Dynamical models for circle covering: Brownian motion and Poisson updatingAnnals of Probability, 36
[Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model. This dynamical model exhibits very interesting behavior. Our goal in this survey is to give an overview of the work in dynamical percolation that has been done (and some of which is in the process of being written up).]
Published: Dec 30, 2009
Keywords: 60K35; Percolation; exceptional times
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