2025/07/22 by Betea, Dan, Nazarov, Anton, Nikitin, Pavel
#05A19 (Secondary) #60C05 (Primary) 60G55 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2507.16320
Last passage percolation (LPP) in an n× n lower triangular domain has nice connections with various generalizations of Schur measures. LPP along an anti-diagonal, from (1,n) to (n,1), gives a distribution of a highest column of a random composition with respect to a Demazure measure (a non-symmetric analog of a Schur measure). LPP along a main diagonal, from (1,1) to (n,n), is distributed as a marginal of a Pfaffian Schur process. In the first case we show that the asymptotics for the constant specialization is governed by the GOE Tracy-Widom distribution, in the second case - by the GSE Tracy-Widom distribution. In the latter case we were also able to study the truncated lower triangular case, obtaining an interesting generalization of the GSE Tracy-Widom distribution.