arXiv subjects

J. Pitman

Publications and source records attributed to J. Pitman.

3 recordsLinked to original sources

arXiv2009

Terrestrial Planet Finder Coronagraph (TPF-C) Flight Baseline Concept

The Terrestrial Planet Finder Coronagraph (TPF-C) mission presented here is an existence proof for a flagship-class internal coronagraph space mission capable of detecting and characterizing Earth-like planets and planetary systems at visible wavelengths around nearby stars, using an existing launch vehicle. TPF-C will use spectroscopy to measure key properties of exoplanets including the presence of atmospheric water or oxygen, powerful signatures in the search for habitable worlds.

astro-ph.IM↗

arXiv2004

Asymptotic laws for regenerative compositions: gamma subordinators and the like

For $\widetilde{\cal R} = 1 - \exp(- {\cal R})$ a random closed set obtained by exponential transformation of the closed range ${\cal R}$ of a subordinator, a regenerative composition of generic positive integer $n$ is defined by recording the sizes of clusters of $n$ uniform random points as they are separated by the points of $\widetilde{\cal R}$. We focus on the number of parts $K_n$ of the composition when $\widetilde{\cal R}$ is derived from a gamma subordinator. We prove logarithmic asymptotics of the moments and central limit theorems for $K_n$ and other functionals of the composition such as the number of singletons, doubletons, etc. This study complements our previous work on asymptotics of these functionals when the tail of the Lévy measure is regularly varying at $0+$.

math.PR↗

arXiv1999

Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions

This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.

math.PR↗