Multiplicative functionals on ensembles of non-intersecting paths
Author(s)Borodin, Alexei; Corwin, Ivan; Remenik, Daniel
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The purpose of this article is to develop a theory behind the occurrence of “path-integral” kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants involving such kernels arise naturally in studying ratios of partition functions and expectations of multiplicative functionals for ensembles of non-intersecting paths on weighted graphs. Our second result shows how Fredholm determinants with extended kernels (as arise in the study of extended determinantal point processes such as the Airy[subscript 2] process) are equal to Fredholm determinants with path-integral kernels. We also show how the second result applies to a number of examples including the stationary (GUE) Dyson Brownian motion, the Airy[subscript 2] process, the Pearcey process, the Airy[subscript 1] and Airy[subscript 2→1] processes, and Markov processes on partitions related to the zz-measures.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Annales de l Institut Henri Poincaré Probabilités et Statistiques
Institute of Mathematical Statistics
Borodin, Alexei, Ivan Corwin, and Daniel Remenik. “Multiplicative Functionals on Ensembles of Non-Intersecting Paths.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 51, no. 1 (February 2015): 28–58. © 2015 Association des Publications de l’Institut Henri Poincaré