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Nathanael Enriquez

Publications and source records attributed to Nathanael Enriquez.

5 recordsLinked to original sources
arXiv2015

Lattice convex chains in the plane

A detailed combinatorial analysis of planar lattice convex polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained. The method which is used emphasizes the connection of the combinatorial analysis with the zeros of the zeta function. It is shown how the Riemann Hypothesis leads to an asymptotic equivalent of the number of convex chains.

math.PR↗
arXiv2013

Spectra of large diluted but bushy random graphs

We compute an asymptotic expansion in $1/c$ of the limit in $n$ of the empirical spectral measure of the adjacency matrix of an Erdős-Rényi random graph with $n$ vertices and parameter $c/n$. We present two different methods, one of which is valid for the more general setting of locally tree-like graphs. The second order in the expansion gives some information about the edge.

math.PR↗
arXiv2008

Renewal series and square-root boundaries for Bessel processes

We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical results by Breiman and Shepp, concerning Brownian motion, and recovers by different means, extensions for Bessel processes, obtained independently by Delong and Yor.

math.PR↗