On the generating function of the Pearcey process

Charlier, Christophe; Moreillon, Philippe

doi:10.48550/arxiv.2107.01859

Cited by 3 publications

(3 citation statements)

References 42 publications

(68 reference statements)

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“…3) for the one-dimensional sine, Airy, Bessel and Pearcey point processes involve explicit constant pre-factors of order 1, and the associated covariances are not small but of order 1, see e.g. [12,14].) In the regime considered here, namely (1.2), the m-point generating function does not decouple as in (1.3), and all joint cumulants of N(r 1 ), .…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 91%

Exponential moments for disk counting statistics of random normal matrices in the critical regime

Charlier¹,

Lenells²

2022

Preprint

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We obtain large n asymptotics for the m-point moment generating function of the disk counting statistics of the Mittag-Leffler ensemble. We focus on the critical regime where all disk boundaries are merging at speed n − 1 2 , either in the bulk or at the edge. As corollaries, we obtain two central limit theorems and precise large n asymptotics of all joint cumulants (such as the covariance) of the disk counting function. Our results can also be seen as large n asymptotics for n × n determinants with merging planar discontinuities.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 91%

Exponential moments for disk counting statistics of random normal matrices in the critical regime

Charlier¹,

Lenells²

2022

Preprint

Self Cite

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“…3) for the onedimensional sine, Airy, Bessel and Pearcey point processes involve explicit constant prefactors of order 1, and the associated covariances are not small but of order 1, see e.g. [14,16].) In the regime considered here, namely (1.2), the m-point generating function does not decouple as in (1.3), and all joint cumulants of N(r 1 ), .…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 92%

Exponential moments for disk counting statistics of random normal matrices in the critical regime

Charlier

Lenells

2023

Nonlinearity

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We obtain large n asymptotics for the m-point moment generating function of the disk counting statistics of the Mittag–Leffler ensemble, where n is the number of points of the process and m is arbitrary but fixed. We focus on the critical regime where all disk boundaries are merging at speed n − 1 2 , either in the bulk or at the edge. As corollaries, we obtain two central limit theorems and precise large n asymptotics of all joint cumulants (such as the covariance) of the disk counting function. Our results can also be seen as large n asymptotics for n × n determinants with merging planar discontinuities.

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“…To derive these large gap asymptotics, however, one needs a deep and strong effort [46]. For the aforementioned various kernels in the form (1.1), the asymptotics of D(I; γ) with I being a single interval can be found in [2,7,23] for the Airy point process, in [11] for the generalized Airy point process, in [8,15,25,32] for the Bessel point process, and in [18,20,21] for the Pearcey process.…”

Section: Introductionmentioning

confidence: 99%

Gap probability for the hard edge Pearcey process

Dang¹,

Xu²,

Zhang³

2022

Preprint

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The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over the interval (0, s) by working on the relevant Fredholm determinants. We establish an integral representation of the gap probability via a Hamiltonian related a system of coupled differential equations. Together with some remarkable differential identities for the Hamiltonian, we derive the large gap asymptotics for the thinned case, up to and including the constant term. As an application, we also obtain the asymptotic statistical properties of the counting function for the hard edge Pearcey process. Contents

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On the generating function of the Pearcey process

Cited by 3 publications

References 42 publications

Exponential moments for disk counting statistics of random normal matrices in the critical regime

Exponential moments for disk counting statistics of random normal matrices in the critical regime

Exponential moments for disk counting statistics of random normal matrices in the critical regime

Gap probability for the hard edge Pearcey process

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