Multiplicative functionals on ensembles of non-intersecting paths
Name
Borodin_Multiplicative functionals.pdf
Size
354.39 KB
Format
Adobe PDF
Checksum (MD5)
2a06162e289f7c0e1fede68b66b30899
Author(s)
Borodin, Alexei
Corwin, Ivan
Remenik, Daniel
Date Issued
February 2015
Journal
Annales de l Institut Henri Poincaré Probabilités et Statistiques
Publisher
Institute of Mathematical Statistics
Citation
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
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/13-AIHP579
