Lectures on integrable probability

zbMath1388.60157arXiv1212.3351MaRDI QIDQ4641985

Alexei Borodin, Vadim Gorin

Publication date: 18 May 2018

Full work available at URL: https://arxiv.org/abs/1212.3351

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Statistical mechanics of polymers (82D60) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (66)

Stochastic six-vertex model ⋮ Bulk universality for random lozenge tilings near straight boundaries and for tensor products ⋮ Markov processes on the duals to infinite-dimensional classical Lie groups ⋮ Interlacing adjacent levels of \(\beta\)-Jacobi corners processes ⋮ The free boundary Schur process and applications. I ⋮ Dynamical correlation functions for products of random matrices ⋮ Interacting particle systems at the edge of multilevel Dyson Brownian motions ⋮ Airy Processes and Variational Problems ⋮ Harold Widom’s work in random matrix theory ⋮ Stochastic Airy semigroup through tridiagonal matrices ⋮ Commentary on “Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem” by David Aldous and Persi Diaconis ⋮ Half-space stationary Kardar-Parisi-Zhang equation ⋮ Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation ⋮ Nonlinear fluctuating hydrodynamics in one dimension: the case of two conserved fields ⋮ The one-dimensional KPZ equation and its universality class ⋮ Stationary half-space last passage percolation ⋮ Multilevel Dyson Brownian motions via Jack polynomials ⋮ A quantization of the harmonic analysis on the infinite-dimensional unitary group ⋮ Some algebraic structures in KPZ universality ⋮ TASEP and generalizations: method for exact solution ⋮ Multicritical random partitions ⋮ Matrix Whittaker processes ⋮ Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point ⋮ KPZ limit theorems ⋮ Integrable fluctuations in the KPZ universality class ⋮ Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique ⋮ Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category ⋮ Determinantal point processes from symplectic and orthogonal characters and applications ⋮ Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution ⋮ Current fluctuations of the stationary ASEP and six-vertex model ⋮ Non-uniqueness times for the maximizer of the KPZ fixed point ⋮ On the exponent governing the correlation decay of the \(\text{Airy}_1\) process ⋮ Stochastic higher spin six vertex model and Macdonald measures ⋮ TASEP fluctuations with soft-shock initial data ⋮ Time-time covariance for last passage percolation with generic initial profile ⋮ Integrable probability: from representation theory to MacDonald processes ⋮ From alternating sign matrices to the Gaussian unitary ensemble ⋮ Monotonous subsequences and the descent process of invariant random permutations ⋮ The KPZ universality class and related topics ⋮ Correlation functions of the Schur process through Macdonald difference operators ⋮ On global solutions of the random Hamilton–Jacobi equations and the KPZ problem ⋮ Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles ⋮ Random sorting networks: local statistics via random matrix laws ⋮ Observables of Macdonald processes ⋮ Universality of local statistics for noncolliding random walks ⋮ Decorated Young tableaux and the poissonized Robinson-Schensted process ⋮ Phase transitions and equilibrium measures in random matrix models ⋮ Statistical properties of eigenvalues of Laplace-Beltrami operators ⋮ Dynamical phase transition of ASEP in the KPZ regime ⋮ On time correlations for KPZ growth in one dimension ⋮ Free field approach to the Macdonald process ⋮ Correlation functions of the Pfaffian Schur process using Macdonald difference operators ⋮ Global fluctuations for multiple orthogonal polynomial ensembles ⋮ Mapping TASEP Back in time ⋮ The intermediate disorder regime for Brownian directed polymers in Poisson environment ⋮ The corner growth model with exponential weights ⋮ Markov dynamics on the dual object to the infinite-dimensional unitary group ⋮ A periodic hexagon tiling model and non-Hermitian orthogonal polynomials ⋮ Correlation functions for determinantal processes defined by infinite block Toeplitz minors ⋮ Stationary stochastic higher spin six vertex model and \(q\)-Whittaker measure ⋮ Limit law of a second class particle in TASEP with non-random initial condition ⋮ Fluctuations of the competition interface in presence of shocks ⋮ Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations ⋮ Height fluctuations for the stationary KPZ equation ⋮ Limit shapes for growing extreme characters of \(U(\infty)\) ⋮ Representations of classical Lie groups and quantized free convolution

Cites Work

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• Solving the KPZ equation
• Log-gamma polymer free energy fluctuations via a Fredholm determinant identity
• Anisotropic growth of random surfaces in \({2+1}\) dimensions
• Directed polymers and the quantum Toda lattice
• Formulas and asymptotics for the asymmetric simple exclusion process
• Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary
• On a classical limit of \(q\)-deformed Whittaker functions
• From duality to determinants for \(q\)-TASEP and ASEP
• \(q\)-distributions on boxed plane partitions
• Exact height distributions for the KPZ equation with narrow wedge initial condition
• Limits of determinantal processes near a tacnode
• Schur dynamics of the Schur processes
• Scaling for a one-dimensional directed polymer with boundary conditions
• Random skew plane partitions with a piecewise periodic back wall
• Yang's system of particles and Hecke algebras
• Strong stationary times via a new form of duality
• Coincidence probabilities
• Random skew plane partitions and the Pearcey process
• On the shuffling algorithm for domino tilings
• Shuffling algorithm for boxed plane partitions
• Large time asymptotics of growth models on space-like paths. I: Push ASEP
• Interaction of Markov processes
• A variational problem for random Young tableaux
• Advanced determinant calculus
• Level-spacing distributions and the Airy kernel
• Scale invariance of the PNG droplet and the Airy process
• Distributions on partitions, point processes, and the hypergeometric kernel
• Elliptically distributed lozenge tilings of a hexagon
• Interpretations of some parameter dependent generalizations of classical matrix ensembles
• Brownian analogues of Burke's theorem.
• Nonintersecting paths, pfaffians, and plane partitions
• Asymptotic theory of characters of the symmetric group
• Non-intersecting paths, random tilings and random matrices
• Determinantal probability measures
• Thoma's theorem and representations of the infinite bisymmetric group
• On orthogonal and symplectic matrix ensembles
• Diffusion of directed polymers in a random environment.
• Shape fluctuations and random matrices
• The continuum directed random polymer
• Limits of multilevel TASEP and similar processes
• Macdonald processes
• The intermediate disorder regime for directed polymers in dimension \(1+1\)
• Moments and Lyapunov exponents for the parabolic Anderson model
• Eigenvalues of GUE minors
• Dyson's Brownian motions, intertwining and interlacing
• Fluctuation properties of the TASEP with periodic initial configuration
• Eynard-Mehta theorem, Schur process, and their Pfaffian analogs
• Die unzerlegbaren, positiv-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe
• Observables of 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
• Statistical Theory of the Energy Levels of Complex Systems. I
• Bethe ansatz replica derivation of the GOE Tracy–Widom distribution in one-dimensional directed polymers with free endpoints
• Lectures on Dimers
• Dynamic Scaling of Growing Interfaces
• Course 1 Random matrices and determinantal processes
• A generalization of MacMahon’s formula
• An Introduction to Random Matrices
• The coincidence approach to stochastic point processes
• On the distribution of the length of the longest increasing subsequence of random permutations
• Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
• Universality of local spectral statistics of random matrices
• Asymptotics of Plancherel measures for symmetric groups
• Random matrices: The Universality phenomenon for Wigner ensembles
• Study of Exactly Soluble One-Dimensional N-Body Problems
• Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension
• Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
• On the Generating Function of a Doubly Infinite, Totally Positive Sequence
• A new class of symmetric functions
• GUEs and queues
• Discrete orthogonal polynomial ensembles and the Plancherel measure
• Infinite wedge and random partitions

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