Asymptotics of free fermions in a quadratic well at finite temperature and the Moshe-Neuberger-Shapiro random matrix model

DOI10.1214/19-AIHP994zbMath1447.82014arXiv1706.06653OpenAlexW3010764995MaRDI QIDQ2179622

Karl Liechty, Dong Wang

Publication date: 13 May 2020

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.06653

zbMATH Keywords

random matricesPoisson processdeterminantal point processTracy-Widom distributionKPZ universalityfree fermions

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Random matrices (algebraic aspects) (15B52) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (11)

Momenta spacing distributions in anharmonic oscillators and the higher order finite temperature Airy kernel ⋮ Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ ⋮ Lower tail of the KPZ equation ⋮ Asymptotics of free fermions in a quadratic well at finite temperature and the Moshe-Neuberger-Shapiro random matrix model ⋮ Lyapunov exponent, universality and phase transition for products of random matrices ⋮ Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation ⋮ On the integrable structure of deformed sine kernel determinants ⋮ The periodic Schur process and free fermions at finite temperature ⋮ Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations ⋮ On the origins of Riemann–Hilbert problems in mathematics* ⋮ Circulant L-ensembles in the thermodynamic limit

Uses Software

• DLMF

Cites Work

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• The transition probability of the \(q\)-TAZRP (\(q\)-bosons) with inhomogeneous jump rates
• Nonintersecting Brownian motions on the unit circle
• Determinantal structures in the O'Connell-Yor directed random polymer model
• From duality to determinants for \(q\)-TASEP and ASEP
• Free fermions and the classical compact groups
• On ASEP with step Bernoulli initial condition
• Tracy-Widom asymptotics for \(q\)-TASEP
• A Fredholm determinant representation in ASEP
• Gaussian and non-Gaussian fluctuations for mesoscopic linear statistics in determinantal processes
• Periodic Airy process and equilibrium dynamics of edge fermions in a trap
• Distributions of a particle's position and their asymptotics in the \(q\)-deformed totally asymmetric zero range process with site dependent jumping rates
• Asymptotics of free fermions in a quadratic well at finite temperature and the Moshe-Neuberger-Shapiro random matrix model
• A phase transition for \(q\)-TASEP with a few slower particles
• From Gumbel to Tracy-Widom
• Macdonald processes
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
• An Introduction to Random Matrices
• Exact results for one-dimensional totally asymmetric diffusion models
• Generalized Ensemble of Random Matrices
• The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process

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