Point processes and the infinite symmetric group.

DOI10.4310/MRL.1998.v5.n6.a9zbMath1044.20501arXivmath/9804088OpenAlexW2017762361MaRDI QIDQ1574674

Alexei Borodin, Grigori Olshanski

Publication date: 13 August 2000

Published in: Mathematical Research Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9804088

Mathematics Subject Classification ID

Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Representations of infinite symmetric groups (20C32) Character groups and dual objects (43A40)

Related Items

Markov processes on partitions ⋮ Markov processes on the duals to infinite-dimensional classical Lie groups ⋮ Correlation kernels for discrete symplectic and orthogonal ensembles ⋮ Giambelli compatible point processes ⋮ Determinantal point processes with \(J\)-Hermitian correlation kernels ⋮ \(\mathfrak{sl}(2)\) operators and Markov processes on branching graphs ⋮ The two-parameter Poisson-Dirichlet point process ⋮ Particle-hole transformation in the continuum and determinantal point processes ⋮ Determinantal Point Processes ⋮ Integral operators, bispectrality and growth of Fourier algebras ⋮ Gaussian limit for determinantal point processes with \(J\)-Hermitian kernels ⋮ Traces on diagram algebras I: Free partition quantum groups, random lattice paths and random walks on trees ⋮ Statistical dynamics of continuous systems: perturbative and approximative approaches ⋮ Discrete gap probabilities and discrete Painlevé equations. ⋮ Random point fields associated with certain Fredholm determinants. I: Fermion, Poisson and Boson point processes. ⋮ The problem of harmonic analysis on the infinite-dimensional unitary group. ⋮ \(J\)-Hermitian determinantal point processes: balanced rigidity and balanced palm equivalence ⋮ The \(z\)-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel ⋮ Quasiregular representations of the infinite-dimensional Borel group ⋮ Dirichlet forms and diffusion processes for fermion random point fields ⋮ Multiplicative functionals on ensembles of non-intersecting paths ⋮ Harmonic analysis on the infinite symmetric group ⋮ Random partitions and the gamma kernel ⋮ \(Z\)-measures on partitions and their scaling limits ⋮ Z-measures on partitions related to the infinite Gelfand pair \((S(2\infty ),H(\infty ))\) ⋮ Pfaffian point processes from free fermion algebras: perfectness and conditional measures ⋮ Glauber dynamics for fermion point processes ⋮ Grigori Iosifovich Olshanski ⋮ Infinite-dimensional diffusions as limits of random walks on partitions ⋮ Kernels and point processes associated with Whittaker functions ⋮ The topological support of the z-measures on the Thoma simplex ⋮ Biorthogonal ensembles ⋮ Determinantal point processes and fermion quasifree states ⋮ Characters of the symmetric groups and correlation functions of point processes ⋮ A Fredholm determinant formula for Toeplitz determinants ⋮ Hua-type integrals over unitary groups and over projective limits of unitary groups ⋮ Conditional intensity and Gibbsianness of determinantal point processes ⋮ Spreading maps (polymorphisms), symmetries of Poisson processes, and matching summation ⋮ The variance of the number of sums of two squares in [inline-graphic 01 [T] in short intervals]