A strict inequality for the random triangle model (2007)
Olle Haggstrom, Tatyana Turova
The random triangle model on a graph G, is a random graph model where the usual i.i.d. measure is perturbed by a factor q t(!), where q 1 is a constant, and t(!) is the number of triangles in the...
We consider the random coloring of the vertices of a graph G, that arises by first performing i.i.d. bond percolation on G, and then assigning a random color, chosen according to some prescribed...
Olle Haggstrom, 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...
Which properties of a random sequence are dynamically sensitive? (2007)
Itai Benjamini, Olle Haggstrom, Yuval Peres, Jeffrey E. Steif
Consider a sequence of i.i.d. random variables, where each variable is refreshed (i.e., replaced by an independent variable with the same law) independently, according to a Poisson clock. At any...
A monotonicity result for hard-core (2007)
and Widom--Rowlinson models on certain d-dimensional lattices
Olle Haggstrom, Johan Jonasson, Russell Lyons
isoperimetric constants and phase transitions in the
On random graph homomorphisms into Z (2007)
Itai Benjamini, Olle Haggstrom, Elchanan Mossel
Given a bipartite connected finite graph G = (V; E) and a vertex v0 2 V, we consider uniform probability measure on the set of graph homomorphisms f: V! Z satisfying f(v0) = 0. This measure can be...
Uniqueness in two-dimensional rigidity percolation (2001)
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...
A note on disagreement percolation (2001)
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...
Olle Haggstrom, 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...
Positive correlations in the fuzzy Potts model (1999)
The fuzzy Potts model arises by taking the q-state Potts model, and then identifying r of the Potts spins with the fuzzy spin 0, and the remaining q \Gamma r Potts spins with the fuzzy spin 1. Here...
We prove uniqueness of the infinite entangled component for bond percolation on the three-dimensional cubic lattice above the entanglement critical probability. This improves earlier results by...
Nonmonotonic behavior in hard-core and Widom-Rowlinson models (1999)
Graham R. Brightwell, Olle Haggstrom, 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...
Nearest-neighbor walks with low predictability profile and percolation (1998)
Olle Haggstrom, 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...
Exact sampling from anti-monotone systems (1997)
Olle Haggstrom, 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....