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Finite Markov Chains and Algorithmic Applications

- Olle Häggström
- Mathematics
- 10 June 2002

1. Basics of probability theory 2. Markov chains 3. Computer simulation of Markov chains 4. Irreducible and aperiodic Markov chains 5. Stationary distributions 6. Reversible Markov chains 7. Markov… Expand

Infinite clusters in dependent automorphism invariant percolation on trees

- Olle Häggström
- Mathematics
- 1 July 1997

We study dependent bond percolation on the homogeneous tree T n of order n ≥ 2 under the assumption of automorphism invariance. Excluding a trivial case, we find that the number of infinite clusters… Expand

Nearest neighbor and hard sphere models in continuum percolation

- Olle Häggström, R. Meester
- Computer Science
- Random Struct. Algorithms
- 1996

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Random-cluster measures and uniform spanning trees

- Olle Häggström
- Mathematics
- 1 October 1995

Consider the random-cluster model on the integer lattice with parameters p and q. As p, q --> 0 in such a way that q/p --> 0, the random-cluster measures converge weakly to the uniform spanning tree… Expand

Monotonicity of uniqueness for percolation on Cayley graphs: all infinite clusters are born simultaneously

- Olle Häggström, Y. Peres
- Mathematics
- 23 February 1999

Abstract. Consider site or bond percolation with retention parameter p on an infinite Cayley graph. In response to questions raised by Grimmett and Newman (1990) and Benjamini and Schramm (1996), we… Expand

Percolation transitive graphs as a coalescent process: relentless merging followed by simultaneous uniqueness

- Olle Häggström, Y. Peres, R. Schonmann
- Mathematics
- 1999

Consider i.i.d. percolation with retention parameter p on an infinite graph G. There is a well known critical parameter p c ∈ [0, 1] for the existence of infinite open clusters. Recently, it has been… Expand

Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model

- Olle Häggström, R. Pemantle
- Mathematics
- 1 December 2000

We study the two-type Richardson model on , d[greater-or-equal, slanted]2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each… Expand

Phase transition in continuum Potts models

- H. Georgii, Olle Häggström
- Mathematics
- 1 November 1996

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… Expand

Coloring percolation clusters at random

- Olle Häggström
- Mathematics
- 1 December 2001

We consider the random coloring of the vertices of a graph G, that arises by first performing i.i.d. bond percolation with parameter p on G, and then assigning a random color, chosen according to… Expand

Instability of matchings in decentralized markets with various preference structures

- Kimmo Eriksson, Olle Häggström
- Mathematics, Computer Science
- Int. J. Game Theory
- 1 March 2008

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