Universal edge scaling in random partitions
Abstract
We establish the universal edge scaling limit of random partitions with the infiniteparameter distribution called the Schur measure. We explore the asymptotic behavior of the wave function, which is a building block of the corresponding kernel, based on the Schrödingertype differential equation. We show that the wave function is in general asymptotic to the Airy function and its higherorder analogs in the edge scaling limit. We construct the corresponding higherorder Airy kernel and the TracyWidom distribution from the wave function in the scaling limit and discuss its implication to the multicritical phase transition in the largesize matrix model. We also discuss the limit shape of random partitions through the semiclassical analysis of the wave function.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 April 2021
 DOI:
 10.1007/s1100502101389y
 arXiv:
 arXiv:2012.06424
 Bibcode:
 2021LMaPh.111...48K
 Keywords:

 Random partition;
 Universal fluctuation;
 Multicritical point;
 Airy kernel;
 TracyWidom distribution;
 Gauge theory;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Combinatorics;
 Mathematics  Probability
 EPrint:
 15 pages