Limit theorems for persistence diagrams

Y Hiraoka, T Shirai, KD Trinh - The Annals of Applied Probability, 2018 - JSTOR
The persistent homology of a stationary point process on RN is studied in this paper. As a
generalization of continuum percolation theory, we study higher dimensional topological …

Rigidity and tolerance in point processes: Gaussian zeros and Ginibre eigenvalues

S Ghosh, Y Peres - 2017 - projecteuclid.org
Let Π be a translation-invariant point process on the complex plane C, and let D⊂ C be a
bounded open set. We ask the following: What does the point configuration Π out obtained …

Rigidity of determinantal point processes with the Airy, the Bessel and the gamma kernel

AI Bufetov - Bulletin of Mathematical Sciences, 2016 - Springer
A point process is said to be rigid if for any bounded domain in the phase space, the number
of particles in the domain is almost surely determined by the restriction of the configuration to …

Absolute continuity and singularity of Palm measures of the Ginibre point process

H Osada, T Shirai - Probability Theory and Related Fields, 2016 - Springer
We prove a dichotomy between absolute continuity and singularity of the Ginibre point
process GG and its reduced Palm measures {G _ x, x ∈ C^ ℓ, ℓ= 0, 1, 2 ...\} G x, x∈ C ℓ, ℓ= 0 …

The sine-process has excess one

AI Bufetov - arxiv preprint arxiv:1912.13454, 2019 - arxiv.org
arxiv:1912.13454v1 [math.PR] 31 Dec 2019 Page 1 arxiv:1912.13454v1 [math.PR] 31 Dec
2019 THE SINE-PROCESS HAS EXCESS ONE ALEXANDER I. BUFETOV ABSTRACT. The …

Approximate Gibbsian structure in strongly correlated point fields and generalized Gaussian zero ensembles

U Gangopadhyay, S Ghosh… - Communications on Pure …, 2024 - Wiley Online Library
Gibbsian structure in random point fields has been a classical tool for studying their spatial
properties. However, exact Gibbs property is available only in a relatively limited class of …

Quasi-symmetries of determinantal point processes

AI Bufetov - arxiv preprint arxiv:1409.2068, 2014 - arxiv.org
The main result of this paper is that determinantal point processes on the real line
corresponding to projection operators with integrable kernels are quasi-invariant, in the …

On the ergodicity of interacting particle systems under number rigidity

K Suzuki - Probability Theory and Related Fields, 2024 - Springer
In this paper, we provide relations among the following properties: the tail triviality of a
probability measure μ on the configuration space Υ; the finiteness of a suitable L 2 …

[PDF][PDF] The conditional measures for the determinantal point process with the Bergman kernel

AI Bufetov - arxiv preprint arxiv:2112.15557, 2021 - arxiv.org
arxiv:2112.15557v1 [math.PR] 31 Dec 2021 Page 1 arxiv:2112.15557v1 [math.PR] 31 Dec
2021 THE CONDITIONAL MEASURES FOR THE DETERMINANTAL POINT PROCESS WITH …

A palm hierarchy for determinantal point processes with the Bessel kernel

AI Bufetov - Proceedings of the Steklov Institute of Mathematics, 2017 - Springer
The main result of this note shows that Palm distributions of the determinantal point process
governed by the Bessel kernel with parameter s are equivalent to the determinantal point …