A Conversation with Shayle R. Searle

Born in New Zealand, Shayle Robert Searle earned a bachelor's degree (1949) and a master's degree (1950) from Victoria University, Wellington, New Zealand. After working for an actuary, Searle went to Cambridge University where he earned a Diploma in mathematical statistics in 1953. Searle won a Fulbright travel award to Cornell University, where he earned a doctorate in animal breeding, with a strong minor in statistics in 1959, studying under Professor Charles Henderson. In 1962, Cornell invited Searle to work in the university's computing center, and he soon joined the faculty as an assistant professor of biological statistics. He was promoted to associate professor in 1965, and became a professor of biological statistics in 1970. Searle has also been a visiting professor at Texas A&M University, Florida State University, Universit\"{a}t Augsburg and the University of Auckland. He has published several statistics textbooks and has authored more than 165 papers. Searle is a Fellow of the American Statistical Association, the Royal Statistical Society, and he is an elected member of the International Statistical Institute. He also has received the prestigious Alexander von Humboldt U.S. Senior Scientist Award, is an Honorary Fellow of the Royal Society of New Zealand and was recently awarded the D.Sc. Honoris Causa by his alma mater, Victoria University of Wellington, New Zealand.Comment: Published in at http://dx.doi.org/10.1214/08-STS259 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Random walks on supercritical percolation clusters

We obtain Gaussian upper and lower bounds on the transition density q_t(x,y) of the continuous time simple random walk on a supercritical percolation cluster C_{\infty} in the Euclidean lattice. The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constants c_i depending only on p (the percolation probability) and d. The irregular nature of the medium means that the bound for q_t(x,\cdot) holds only for t\ge S_x(\omega), where the constant S_x(\omega) depends on the percolation configuration \omega.Comment: Published at http://dx.doi.org/10.1214/009117904000000748 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Real-time simulation of finite frequency noise from a single electron emitter

We study the real-time emission of single electrons from a quantum dot coupled to a one dimensional conductor, using exact diagonalization on a discrete tight-binding chain. We show that from the calculation of the time-evolution of the one electron states, we have a simple access to all the relevant physical quantities in the system. In particular, we are able to compute accurately the finite frequency current autocorrelation noise. The method which we use is general and versatile, allowing to study the impact of many different parameters like the dot transparency or level position. Our results can be directly compared with existing experiments, and can also serve as a basis for future calculations including electronic interactions using the time dependent density-matrix renormalisation group and other techniques based on tight-binding models.Comment: 10 page

On the Reliability of the Langevin Pertubative Solution in Stochastic Inflation

A method to estimate the reliability of a perturbative expansion of the stochastic inflationary Langevin equation is presented and discussed. The method is applied to various inflationary scenarios, as large field, small field and running mass models. It is demonstrated that the perturbative approach is more reliable than could be naively suspected and, in general, only breaks down at the very end of inflation.Comment: 7 pages, 3 figure

Energy inequalities for cutoff functions and some applications

We consider a metric measure space with a local regular Dirichlet form. We establish necessary and sufficient conditions for upper heat kernel bounds with sub-diffusive space-time exponent to hold. This characterization is stable under rough isometries, that is it is preserved under bounded perturbations of the Dirichlet form. Further, we give a criterion for stochastic completeness in terms of a Sobolev inequality for cutoff functions. As an example we show that this criterion applies to an anomalous diffusion on a geodesically incomplete fractal space, where the well-established criterion in terms of volume growth fails