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41st Annual Symposium on Foundations of Computer Science
Sampling adsorbing staircase walks using a new Markov chain decomposition method
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
R.A. Martin, D. Randall, "Sampling adsorbing staircase walks using a new Markov chain decomposition method," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 492, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892137, author = {R.A. Martin and D. Randall}, title = {Sampling adsorbing staircase walks using a new Markov chain decomposition method}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {492}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892137}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Sampling adsorbing staircase walks using a new Markov chain decomposition method SN  02725428 SP EP A1  R.A. Martin, A1  D. Randall, PY  2000 KW  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 VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
Staircase walks are lattice paths from (0,0) to (2n,0) which take diagonal steps and which never fall below the xaxis. A path hitting the xaxis /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, pp.492, 41st Annual Symposium on Foundations of Computer Science, 2000
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