Some two-dimensional finite energy percolation processes (2009)
Häggström, Olle; Chalmers University Of Technology; Olleh@chalmers.se, Mester, Péter; Indiana University; Pmester@indiana.edu
Some examples of translation invariant site percolation processes on the $Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the...
Localized techniques for broadcasting in wireless sensor networks.” Algorithmica (2008)
Devdatt Dubhashi, Olle Häggström, Lorenzo Orecchia, Chiara Petrioli, Andrea Vitaletti
Abstract. In this paper we tackle the problem of designing simple, localized, low energy consuming, reliable protocols for one-to-all communication in large scale wireless sensor networks. Our first...
Instability of matchings in decentralized (2008)
Kimmo Eriksson, Olle Häggström, Kimmo Eriksson, Olle Häggström
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Instability of matchings in decentralized (2008)
Kimmo Eriksson, Olle Häggström, Kimmo Eriksson, Olle Häggström
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Sannolikhetsteori På Tvåvåningsgrafer (2007)
e vag fran (u; 0) till (v; 0) ar ett steg kortare an kortaste vag fran (u; 0) till (v; 1). Man kan tanka sig andra de nitioner av "narhet", men det ligger nara till hands att tanka...
On Variance Conditions for Markov Chain CLTs 1. Introduction. by (2007)
Olle Häggström, Jeffrey S. Rosenthal
The existence of central limit theorems (CLTs) for Markov chains is well studied, and
On Variance Conditions for Markov Chain CLTs 1. Introduction. by (2007)
Olle Häggström, Jeffrey S. Rosenthal
The existence of central limit theorems (CLTs) for Markov chains is well studied, and
The volume fraction of a non--overlapping germ--grain model (2006)
Andersson, Jenny; Mathematical Sciences, Chalmers University Of Technology; Jennya@math.chalmers.se, Häggström, Olle; Mathematical Sciences, Chalmers University Of Technology; Olleh@math.chalmers.se, Månsson, Marianne; Mathematical Sciences, Chalmers University Of Technology; Marianne@math.chalmers.se
We discuss the volume fraction of a model of non--overlapping convex grains. It is obtained from thinning a Poisson process where each point has a weight and is the centre of a grain, by removing any...
Uniqueness of Infinite Rigid Components in Percolation Models: The Case of Nonplanar Lattices (2003)
We prove uniqueness of the infinite rigid component for standard bond percolation on periodic lattices in d-dimensional Euclidean space for arbitrary d, and more generally when the lattice is a...
A Stochastic Model for Competing Growth on R^d (2003)
Maria Deijfen, Olle Häggström, Jonathan Bagley
A stochastic model, describing the growth of two competing infections , is introduced. The growth is driven by outbursts in the infected region, an outburst in the type 1 (2) infected region...
The two-type Richardson model describes the growth of two competing infections on Z . At time 0 two disjoint finite sets #1 , #2 are infected with type 1 and type 2 infection respectively. An...
Häggström, Olle; Chalmers University Of Technology And Goteborg University; Olleh@math.chalmers.se
For each $dgeq 2$, we give examples of $d$-dimensional periodic lattices on which the hard-core and Widom-Rowlinson models exhibit a phase transition which is monotonic, in the sense that there...
Is the fuzzy Potts model Gibbsian? (2002)
The fuzzy Potts model is obtained by looking at the Potts model with a pair of glasses that prevents distinguishing between some of the spin values. We show that the fuzzy Potts model on Z (d 2) is...
Zero-Temperature Dynamics for the Ferromagnetic Ising Model on Random Graphs (2002)
We consider Glauber dynamics at zero temperature for the ferromagnetic Ising model on the usual random graph model on N vertices, with on average fl edges incident to each vertex, in the limit as N !...
Coupling and Bernoullicity in Random-cluster and Potts Models (2001)
Olle Häggström, Johan Jonasson, Russell Lyons
An explicit coupling construction of random-cluster measures is presented. As one of the applications of the construction, the Potts model on amenable Cayley graphs is shown to exhibit at every...
Explicit Isoperimetric Constants and Phase Transitions in the Random-Cluster Model (2001)
Olle Häggström, Johan Jonasson, Russell Lyons
The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on...
Finite Markov Chains and Algorithmic Applications (2000)
CONTENTS 0 PREFACE 3 1 BASICS OF PROBABILITY THEORY 5 2 MARKOV CHAINS 9 3 COMPUTER SIMULATION OF MARKOV CHAINS 16 4 IRREDUCIBLE AND APERIODIC MARKOV CHAINS 22 5 STATIONARY DISTRIBUTIONS 27 6...
A Note on Disagreement Percolation (2000)
We construct a coupling of two distinct Gibbs measures for Markov random fields with the same specifications, such that the existence of an infinite path of disagreements between the two...
Benjamini, Itai, Häggström, Olle, Schramm, Oded
We show that adding epsilon-Bernoulli percolation to an everywhere percolating subgraph of Z^2 results in a graph which has large scale geometry similar to that of supercritical Bernoulli...
Propp-Wilson algorithms and finitary codings for high noise Markov random fields (1999)
Olle Häggström, Jeffrey E. Steif
In this paper, we combine two previous works, the first being by the first author and K. Nelander, and the second by J. van den Berg and the second author, to show (1) that one can carry out a...
Olle Häggström, Robin Pemantle
We study the two-type Richardson model on Z , d 2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the...
The Ising Model on Diluted Graphs and Strong Amenability (1999)
Olle Häggström, Roberto H. Schonmann, Jeffrey E. Steif
Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external eld. We show that for...
Olle Häggström, Robin Pemantle
We study the two-type Richardson model on Z d , d 2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the...
Uniqueness in Two-Dimensional Rigidity Percolation (1999)
For bond percolation on the two-dimensional triangular lattice with arbitrary retention parameter p 2 [0; 1], we show that the number of infinite rigid components is a.s. at most one. This proves a...
Itai Benjamini, Olle Häggström, Oded Schramm
We show that adding -Bernoulli percolation to an everywhere percolating subgraph of Z 2 results in a graph which has large scale geometry similar to that of supercritical Bernoulli percolation, in...
Itai Benjamini, Olle Häggström, Oded Schramm
We show that adding ffl-Bernoulli percolation to an everywhere percolating subgraph of Z 2 results in a graph which has large scale geometry similar to that of supercritical Bernoulli percolation, in...
Markov Random Fields and Percolation on General Graphs (1999)
Let G be an infinite, locally finite, connected graph with bounded degree. We show that G supports phase transition in all or none of the following five models: bond percolation, site percolation,...
Olle Häggström, Robin Pemantle
We study the two-type Richardson model on Z d , d 2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the...
The Random Geometry of Equilibrium Phases (1999)
Hans-otto Georgii, Olle Häggström, Christian Maes
this report. We are also grateful to L. Chayes, A.C.D. van Enter and J. Lorinczi who looked at parts of the manuscript and made numerous suggestions, and to Y. Higuchi for discussions on Proposition...
The Ising Model on Diluted Graphs and Strong Amenability (1999)
Olle Häggström, Roberto H. Schonmann, Jeffrey E. Steif
Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external field. We show that...
Nearest-neighbor walks with low predictability profile and percolation (1998)
Olle Häggström, Elchanan Mossel
A few years ago, Grimmett, Kesten and Zhang proved that for supercritical bond percolation on Z 3, simple random walk on the infinite cluster is a.s. transient. We generalize this result to a class...
On random graph homomorphisms into Z (1998)
Itai Benjamini, Olle Häggström, Elchanan Mossel
Given a bipartite connected finite graph G = (V; E) and a vertex v 0 2 V , we consider uniform probability measure on the set of graph homomorphisms f : V ! Z satisfying f(v 0 ) = 0. This measure can...
Nonmonotonic behavior in hard-core and Widom-Rowlinson models (1998)
Graham Brightwell, Olle Häggström, Peter Winkler
We give two examples of nonmonotonic behavior in symmetric systems, exhibiting more than one critical point at which spontaneous symmetry-breaking appears or disappears. The two systems are the...
Exact Sampling From Anti-Monotone Systems (1997)
Olle Häggström, Karin Nelander
A new approach to Markov chain Monte Carlo simulation was recently proposed by Propp and Wilson. This approach, unlike traditional ones, yields samples which have exactly the desired distribution....
Phase Transition in Continuum Potts Models (1996)
Hans-otto Georgii, Olle Häggström
We establish phase transitions for a class of continuum multi--type particle systems with finite range repulsive pair interaction between particles of different type. This proves an old conjecture of...
Olle Häggström, Yuval Peres, Jeffrey E. Steif
We study bond percolation evolving in time in such a way that the edges turn on and off independently according to a continuous time stationary 2-state Markov chain. Asking whether an infinite open...
Instability of matchings in decentralized markets with various preference structures
Kimmo Eriksson, Olle Häggström
Stable matching, Blocking pair, Instability, Preference structure, Decentralized market, Maximin matching,