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Large gap asymptotics for the generating function of the sine point process.

Christophe Charlier1

  • 1Department of Mathematics KTH Royal Institute of Technology Lindstedtsvägen 25 Stockholm SE-114 28 Sweden.

Proceedings of the London Mathematical Society
|October 15, 2021
PubMed
Summary
This summary is machine-generated.

This study analyzes the sine point process generating function, providing new insights into large gap asymptotics. The findings generalize existing results and offer applications in process thinning and conditioning.

Keywords:
35Q15 (primary)41A6060B2060G55 (secondary)

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Area of Science:

  • Probability Theory
  • Mathematical Physics

Background:

  • The sine point process is a key model in random matrix theory and statistical physics.
  • Its generating function, often expressed as a Fredholm determinant, is crucial for understanding process properties.
  • Existing research has established results for specific parameter values.

Purpose of the Study:

  • To derive large gap asymptotics for the sine point process generating function.
  • To generalize known results for specific parameter regimes.
  • To explore applications in process thinning and conditioning.

Main Methods:

  • Utilizing the Fredholm determinant representation of the generating function.
  • Employing series expansions for asymptotic analysis.
  • Analyzing cases with arbitrary integer parameters and specific positivity conditions.

Main Results:

  • Obtained novel large gap asymptotic formulas for the generating function.
  • Generalized previously known results by Basor and Widom and others.
  • Demonstrated validity for a broad range of parameters.

Conclusions:

  • The derived asymptotics provide a deeper understanding of the sine point process behavior.
  • The generalization extends the applicability of theoretical results.
  • Applications in thinning and conditioning highlight practical relevance.