Exponential convergence to equilibrium for a class of random-walk models

Journal Article · Wed Feb 01 04:00:00 EST 1989 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01019776· OSTI ID:5626982

Sokal, A D; Thomas, L E

The authors prove exponential convergence to equilibrium (L/sup 2/ geometric ergodicity) for a random walk with inward drift on a sub-Cayley rooted tree. This random walk model generalizes a Monte Carlo algorithm for the self-avoiding walk proposed by Berretti and Sokal. If the number of vertices of level N in the tree grows as c/sub N/ /approx/ /mu//sup N/N/sup /gamma/minus/1//, they prove that the autocorrelation time /tau/ satisfies /sup 2/ /approx lt/ /tau/ /approx lt/ /sup 1 + /gamma//.

• Research Organization: New York Univ., NY (USA)
• OSTI ID: 5626982
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 54:3-4; ISSN JSTPB
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
BANACH SPACE
BOUNDARY CONDITIONS
CONVERGENCE
CORRELATION FUNCTIONS
CRITICAL PRESSURE
CRITICAL TEMPERATURE
DYNAMICS
FIELD THEORIES
FUNCTIONS
GRAPHS
HILBERT SPACE
LYAPUNOV METHOD
MARKOV PROCESS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATRICES
MECHANICS
MONTE CARLO METHOD
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
RANDOMNESS
RITZ METHOD
SPACE
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
THERMODYNAMIC PROPERTIES
TIME DEPENDENCE
TRANSITION TEMPERATURE
TRANSPORT THEORY