6533b872fe1ef96bd12d3880
RESEARCH PRODUCT
Juggler's exclusion process
Lasse LeskeläHarri Varpanensubject
Statistics and Probabilityset-valued Markov processmaximum entropy60K35 82C41General Mathematics82C41FOS: Physical sciencesMarkov process01 natural sciencespositive recurrencesymbols.namesakeGravitational potentialMarkov renewal process0103 physical sciencesjuggling patternFOS: MathematicsErgodic theory0101 mathematicsGibbs measureMathematical PhysicsMathematicsDiscrete mathematicsnoncolliding random walkProbability (math.PR)ta111010102 general mathematicsErgodicityMathematical analysisExclusion processMathematical Physics (math-ph)Gibbs measureDistribution (mathematics)set-avoiding memoryless distribution60K35Jumpsymbolsergodicity010307 mathematical physicsStatistics Probability and UncertaintyMathematics - Probabilitydescription
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-03-01 |