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March 10, 2026Journal of the London Mathematical Society0 citations

Airy wanderer line ensembles

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EDEvgeni Dimitrov

Key Points

  • The aim is to construct determinantal point processes using generalized Airy kernels and to establish the Brownian Gibbs property for specific parameter choices.
  • Constructed determinantal point processes based on generalized Airy kernels.
  • Analyzed a subset of parameter space to lift point processes to line ensembles.
  • Studied the characteristics of line ensembles for the Brownian Gibbs property.
  • Establishes a framework for variable parameter settings in point processes.
  • Demonstrates that line ensembles can be constructed under specific conditions.
  • Confirms that these ensembles satisfy the Brownian Gibbs property.

Abstract

Abstract In (J. Stat. Phys. 132 , 275–290, 2008), Borodin and Péché introduced a generalization of the extended Airy kernel based on two infinite sets of parameters. For an arbitrary choice of parameters, we construct determinantal point processes on for these generalized kernels. In addition, for a subset of the parameter space, we show that the point processes can be lifted to line ensembles on , which satisfy the Brownian Gibbs property. Our ensembles generalize the wanderer line ensembles introduced by Corwin and Hammond (Invent. Math. 195 , 441–508, 2014).

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Cite This Study

Evgeni Dimitrov (2026) studied this question.

synapsesocial.com/papers/69af952b70916d39fea4c781https://doi.org/10.1112/jlms.70482
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