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Redondo Beach, California

Nov. 12, 2000 to Nov. 14, 2000

ISBN: 0-7695-0850-2

pp: 492

R.A. Martin , Sch. of Math., Georgia Inst. of Technol., Atlanta, GA, USA

D. Randall , Sch. of Math., Georgia Inst. of Technol., Atlanta, GA, USA

ABSTRACT

Staircase walks are lattice paths from (0,0) to (2n,0) which take diagonal steps and which never fall below the x-axis. A path hitting the x-axis /spl kappa/ times is assigned a weight of /spl lambda//sup /spl kappa//, where /spl lambda/<0. A simple local Markov chain, which connects the state space and converges to the Gibbs measure (which normalizes these weights) is known to be rapidly mixing when /spl lambda/=1, and can easily be shown to be rapidly mixing when /spl lambda/>1. We give the first proof that this Markov chain is also mixing in the more interesting case of /spl lambda/<1, known in the statistical physics community as adsorbing staircase walks. The main new ingredient is a decomposition technique which allows us to analyze the Markov chain in pieces, applying different arguments to analyze each piece.

INDEX TERMS

Markov processes; theorem proving; lambda calculus; adsorbing staircase walks; Markov chain decomposition method; lattice paths; diagonal steps; local Markov chain; state space; /spl lambda//sup /spl kappa//; Gibbs measure; first proof; Markov chain; statistical physics community; decomposition technique

CITATION

R.A. Martin,
D. Randall,
"Sampling adsorbing staircase walks using a new Markov chain decomposition method",

*FOCS*, 2000, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2000, pp. 492, doi:10.1109/SFCS.2000.892137