QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

Determination of controls on Holocene barrier progradation through application of OSL dating: The Ilha Comprida Barrier example, Southeastern Brazil

Barrier development during the Holocene is studied using the example of the Ilha Comprida, Southeastern Brazil. Aerial photos, facies analysis, and optically stimulated luminescence dating are used to define the barrier emergence and evolution. Optically stimulated luminescence ages and facies successions indicate that the Ilha Comprida probably began as a Holocene transgressive barrier island 6000 years ago, just before the last relative sea-level maximum. Since then the barrier has progradated through the addition of curved beach ridges. Based on beach ridge alignments, six units of growth are identified with two growth directions, transverse and longitudinal. Rates of progradation with transverse growth vary from 0.13 to 4.6 m/year. Rates of longitudinal growth to NE range from 5.2 to 30 m/year. Variation in coastal progradation rates and sediment retention during the last 6000 years is compared with climate, physiography and relative sea-level changes. The physiography, represented by pre-Cenozoic hills, is the major control on sediment retention and alternation between longitudinal and transverse growth. Climate variations, such as the Little Ice Age event, apparently control the formation of ridges types: beach ridges, foredunes, and blowouts. These results allow the use of the Ilha Comprida Barrier as an example to analyze the major controls on barriers progradation. (C) 2011 Elsevier B.V. All rights reserved.