8 papers
Number variance for homogeneous determinantal processes on hyperbolic spaces
Pierre Lazag
We consider an abstract determinantal point process on a general non--elementary Gromov hyperbolic metric space governed by an orthogonal projection in the case when the space is h…
Accumulated spectrograms for hyperuniform determinantal point processes
Makoto Katori, Pierre Lazag, Tomoyuki Shirai
We define the accumulated spectrogram associated to a locally trace class orthogonal projection operator and to a bounded set using the polar decomposition of its restriction on th…
The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures
Pierre Lazag
We prove Fredholm determinants build out from generalizations of Schur measures, or equivalently, arbitrary multiplicative statistics of the original Schur measures are tau-functio…
A law of large numbers for local patterns in Schur measures and a Schur process
Pierre Lazag
The aim of this note is to prove a law of large numbers for local patterns in discrete point processes. We investigate two different situations: a class of point processes on the o…
A determinantal point process governed by an integrable projection kernel is Giambelli compatible
Alexander I. Bufetov, Pierre Lazag
The first main result of this note, Theorem 1.2, establishes the determinantal identities (7) and (8) for the expectation, under a determinantal point process governed by an integr…
A law of large numbers for local patterns in plane partitions
Pierre Lazag
In this note, we prove a law of large numbers for local patterns in plane partitions with geometric weight, a model introcued by Okounkov and Reshetikhin. Its proof is based on the…
Explicit description of Christoffel deformations and Palm measures of the Plancherel measure, the -measures and the Gamma process
Pierre Lazag
Christoffel deformation of a measure on the real line consists of multipying this measure by a squared polynomial having its roots in . We introduce Christoffel deformations of…
The Hyperbolic-type Point Process
Nizar Demni, Pierre Lazag
In this paper, we introduce a two-parameters determinantal point process in the Poincaré disc and compute the asymptotics of the variance of its number of particles inside a disc c…