The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem.

The Bessel process models the local eigenvalue statistics near $0$ of certain large positive definite matrices. In this work, we consider the probability \begin{align*} \mathbb{P}\Big( \mbox{there are no points in the Bessel process on } (0,x_{1})\cup(x_{2},x_{3})\cup\cdots\cup(x_{2g},x_{2g+1}) \Big), \end{align*} where $0

Keywords:

• Bessel process
• Riemann hypothesis
• Bessel function
• Pure mathematics
• Almost surely
• Diophantine equation
• Ergodic theory
• Riemann surface
• Mathematics
• Positive-definite matrix

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