Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
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
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.
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
R. Martin and D. Randall, "Sampling adsorbing staircase walks using a new Markov chain decomposition method," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 492.