Determinantal transition kernels for some interacting particles on the line

DOI10.1214/07-AIHP176zbMath1181.60144arXiv0707.1843MaRDI QIDQ731723

A. B. Dieker, Jon Warren

Publication date: 8 October 2009

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1843

zbMATH Keywords

symmetric functionsintertwininginteracting particle systemRobinson-Schensted-Knuth correspondencestochastic recursionKarlin-McGregor theoremMarkov transition kernelSchütz theorem

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Discrete-time Markov processes on general state spaces (60J05) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (15)

On inhomogeneous polynuclear growth ⋮ A multi-dimensional Markov chain and the Meixner ensemble ⋮ Anisotropic growth of random surfaces in \({2+1}\) dimensions ⋮ TASEP and generalizations: method for exact solution ⋮ Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point ⋮ On the KPZ scaling and the KPZ fixed point for TASEP ⋮ Free fermions and canonical Grothendieck polynomials ⋮ Exact solution of interacting particle systems related to random matrices ⋮ Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions ⋮ PushTASEP in inhomogeneous space ⋮ Interlacing Diffusions ⋮ Generalizations of TASEP in discrete and continuous inhomogeneous space ⋮ The invariant measure of PushASEP with a wall and point-to-line last passage percolation ⋮ Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy-Widom GOE distribution ⋮ The two-time distribution in geometric last-passage percolation

Cites Work

• Multiparticle space-time transitions in the totally asymmetric simple exclusion process
• Integral formulas for the asymmetric simple exclusion process
• Orthogonal polynomial ensembles in probability theory
• Large time asymptotics of growth models on space-like paths. I: Push ASEP
• Matrix correspondences of plane partitions
• Exact solution of the master equation for the asymmetric exclusion process
• Exact limiting shape for a simplified model of first-passage percolation on the plane
• Current distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Shape fluctuations and random matrices
• A multi-dimensional Markov chain and the Meixner ensemble
• Dyson's Brownian motions, intertwining and interlacing
• Fluctuation properties of the TASEP with periodic initial configuration
• Series Jackson Networks and Noncrossing Probabilities
• A path-transformation for random walks and the Robinson-Schensted correspondence
• Conditioned random walks and the RSK correspondence
• Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates
• Queues, stores, and tableaux
• GUEs and queues
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