Infinite-dimensional diffusions as limits of random walks on partitions

The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group. This problem leads to a family {P_z} of probability measures, the z-measures, which depend on the complex parameter z. The z-measures live on the Thoma simplex, an infinite-dimensional compact space which is a kind of dual object to the infinite symmetric group. The aim of the paper is to introduce stochastic dynamics related to the z-measures. Namely, we construct a family of diffusion processes in the Toma simplex indexed by the same parameter z. Our diffusions are obtained from certain Markov chains on partitions of natural numbers n in a scaling limit as n goes to infinity. These Markov chains arise in a natural way, due to the approximation of the infinite symmetric group by the increasing chain of the finite symmetric groups. Each z-measure P_z serves as a unique invariant distribution for the corresponding diffusion process, and the process is ergodic with respect to P_z. Moreover, P_z is a symmetrizing measure, so that the process is reversible. We describe the spectrum of its generator and compute the associated (pre)Dirichlet form.Comment: AMSTex, 33 pages. Version 2: minor changes, typos corrected, to appear in Prob. Theor. Rel. Field

Substantial secondary organic aerosol formation in a coniferous forest: Observations of both day- and nighttime chemistry

10.5194/acp-16-6721-2016Atmospheric Chemistry and Physics16116721-673

Glucosinolate Breakdown in Arabidopsis: Mechanism, Regulation and Biological Significance

Glucosinolates are a group of thioglucosides in plants of the Brassicales order. Together with their hydrolytic enzymes, the myrosinases, they constitute the ‘mustard oil bomb’ involved in plant defense. Here we summarize recent studies in Arabidopsis that have provided molecular evidence that the glucosinolate-myrosinase system is much more than a ‘two-component defense system,’ and started to unravel the roles of different glucosinolate breakdown pathways in the context of plant responses to biotic and abiotic stresses