Reda Chhaibi

On the maximum of the C

In this paper, we investigate the extremal values of (the logarithm of) the characteristic polynomial of a random unitary matrix whose spectrum is distributed according the Circular Beta Ensemble (C

\beta

\beta

E field

E). More precisely, if

Non-Archimedean Whittaker Functions as Characters: A Probabilistic Approach to the Shintani–Casselman–Shalika Formula

X_n

Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion

is this characteristic polynomial and

The circular unitary ensemble and the Riemann zeta function: the microscopic landscape and a new approach to ratios

\mathbb{U}

Littelmann path model for geometric crystals

the unit circle, we prove that:

Whittaker processes and Landau-Ginzburg potentials for flag manifolds

\sup_{z \in \mathbb{U} } \Re \log X_n(z) = \sqrt{\frac{2}{\beta}} \left(\log n - \frac{3}{4} \log \log n + \mathcal{O}(1) \right)\ ,