LARGE DEVIATIONS FOR THE q-DEFORMED POLYNUCLEAR GROWTH

• 成果类型: Article
• 署名作者: Das, Sayan; Liao, Yuchen; Mucciconi, Matteo
• 署名单位: Columbia University; Chinese Academy of Sciences; University of Science & Technology of China, CAS; National University of Singapore
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1733
• 发表日期: 2025
• 页码: 1223-1286
• 关键词: model; asymptotics; fluctuations; determinants; analogs; energy; edge; tail

摘要

In this paper we study large time large deviations for the height function h(x, t) of the q-deformed polynuclear growth introduced in (Int. Math. Res. Not. IMRN 7 (2023) 5728-5780). We show that the upper-tail deviations have speed t and derive an explicit formula for the rate function Phi+(mu). On the other hand, we show that the lower-tail deviations have speed t2 and express the corresponding rate function Phi-(mu) in terms of a variational problem. Our analysis relies on distributional identities between the height function h and two important measures on the set of integer partitions: the Poissonized Plancherel measure and the cylindric Plancherel measure. Following a scheme developed in (Ann. Inst. Henri Poincar & eacute; Probab. Stat. 57 (2021) 778-799), we analyze a Fredholm determinant representation for the q-Laplace transform of h(x, t) from which we extract exact Lyapunov exponents and through inversion the upper-tail rate function Phi+. The proof of the lower-tail large deviation principle is more subtle and requires several novel ideas which combine classical asymptotic results for the Plancherel measure and log-concavity properties of Schur polynomials. The techniques we develop to characterize the lower-tail are rather flexible and have the potential to generalize to other solvable growth models.