Exit problems associated with affine reflection groups

We obtain a formula for the distribution of the first exit time of Brownian motion from the alcove of an affine Weyl group. In most cases the formula is expressed compactly, in terms of Pfaffians. Expected exit times are derived in the type \~A case. The results extend to other Markov processes. We also give formulas for the real eigenfunctions of the Dirichlet and Neumann Laplacians on alcoves, observing that the `Hot Spots' conjecture of J. Rauch is true for alcoves.Comment: 34 pages. Rewritten in some places to improve presentation. To appear in Probability Theory and Related Field

On the free energy of a directed polymer in a Brownian environment

We prove a formula conjectured in O'Connell and Yor (2001) for the free energy density of a directed polymer in a Brownian environment in 1+1 dimensions.Comment: 15 pages. To appear in Markov Processes and Related Filelds (J.T. Lewis special edition

Evolutionary Inference for Function-valued Traits: Gaussian Process Regression on Phylogenies

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical model for such data, by combining assumptions from phylogenetics with Gaussian processes. We describe its use as a nonparametric Bayesian prior distribution, both for prediction (placing posterior distributions on ancestral functions) and model selection (comparing rates of evolution across a phylogeny, or identifying the most likely phylogenies consistent with the observed data). Our work is integrative, extending the popular phylogenetic Brownian Motion and Ornstein-Uhlenbeck models to functional data and Bayesian inference, and extending Gaussian Process regression to phylogenies. We provide a brief illustration of the application of our method.Comment: 7 pages, 1 figur

University Library Development in Indiana, 1910 to 1966

published or submitted for publicatio

Division benchmarks for New Zealand tourism characteristic and tourism related industries 2000-2004

Performance monitoring and benchmarking are important contributors to policy and planning processes. Tourism presents particular challenges as visitor expenditure supports a broad spectrum of commercial activity throughout hundreds of the economy’s industrial divisions. It has been difficult to establish financial performance benchmarks at divisional level because enterprise performance is generally confidential (unless required to be disclosed – e.g. as part of an obligation to list on a public exchange such as NZX). More easily identified alternatives are generally activity based (e.g. revenues, customer volumes, market share) and whilst useful they offer no insight into financial or economic performance. The benchmarking metrics in this report include Financial Yield (FY) and a variety of operating ratios based on revenue. These benchmarks represent the consolidated financial performance of enterprise business units within New Zealand Tourism’s characteristic and related industries. They reflect the degree to which divisions generate wealth (Financial Yield) and report the operating parameters associated with that performance