Joseph Najnudel

A global view of Brownian penalisations

The present volume is an expository monograph on Brownian penalisation, an important new notion the authors introduced to the theory of Wiener measure and Markov processes. It will serve as a concise guidebook for students and researchers who study probability theory, stochastic processes and mathematical finance.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

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

On Some Properties of Universal Sigma-Finite Measures Associated with a Remarkable Class of Submartingales

X_n

RANDOM PERMUTATION MATRICES UNDER THE GENERALIZED EWENS MEASURE

is this characteristic polynomial and

A Remarkable σ-finite Measure Associated with Last Passage Times and Penalisation Problems

\mathbb{U}

Scaled Limit and Rate of Convergence for the Largest Eigenvalue from the Generalized Cauchy Random Matrix Ensemble

the unit circle, we prove that:

On a Flow of Operators Associated to Virtual Permutations

\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)\ ,