Noticias en español
Quantum Turbulence and the Gross-Pitaevskii Equation
Abstract: The talk will start by a brief introduction to physical systems displaying regimes of quantum turbulence. The status of several standard models of superfluidity will then be discussed. The rest of the talk will concentrate on models based on the Gross-Pitaevskii equation (GPE). At first sight, the GPE can only describe a vanishing-temperature dilute superfluid. We will explain how these limitations can be lifted and how finite-temperature effects can be obtained by using classical-field models such as the Galerkin-truncated GPE. The basic numerical tools needed to properly...
Read MoreNon-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble
Resumen: Consider N non-intersecting Brownian bridges, all starting from 0 at time t = 0 and returning to 0 at time t = 1. The Airy_2 process is defined as the motion of the top path (suitably rescaled) in the large N limit. K. Johansson proved the remarkable fact that the supremum of the Airy_2 process minus a parabola has the Tracy-Widom GOE distribution from random matrix theory. In this talk, I will present a result which shows that the squared maximal height of the top path in the case of finite N is distributed as the top eigenvalue of a random matrix drawn from the Laguerre Orthogonal...
Read MoreDeep factorization of the stable process
Abstract: The Lamperti–Kiu transformation for real-valued self-similar Markov processes (rssMp) states that, associated to each rssMp via a space-time transformation, is a Markov additive process (MAP). In the case that the rssMp is taken to be an α-stable process with α ∈ (0,2), the characteristics of the matrix exponent of the semi-group of the embedded MAP (the Lamperti-stable MAP) are computed. Specifically, the matrix exponent of the Lamperti-stable MAP’s transition semi-group can be written in a compact form using only gamma functions. Just as with Levy processes, there exists a...
Read MoreA non exchangeable coalescent arising in phylogenetics
Abstract: A popular line of research in evolutionary biology is to use time-calibrated phylogenies in order to infer the underlying diversification process. Most models of diversification assume that species are exchangeable and lead to phylogenetic trees whose shape is the same in distribution as that of a Yule pure-birth tree. Here, we propose a non-exchangeable, individual-based, point mutation model of diversification where interspecific pairwise competition (rate d) is always weaker than intraspecific pairwise competition (rate c), and is only felt from the part of individuals belonging...
Read MoreCollap transition of a self-interacting partially directed random walk.
Abstract: We investigate the 1 + 1 dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The IPDSAW is known to undergo a extended-collapsed transition at a critical point \beta_c. We present here a new method that provides a probabilistic representation of the partition function, from which we derive a variational formula for the free energy. This variational formula allows us to prove the existence of the collapse transition and to identify the critical point in a simple way. We also provide the precise asymptotic of the free...
Read MoreExponential Familia Techniques for the Lognormal Left Tail
ABSTRACT: Sums of lognormals random variables arise in a wide variety of disciplines such as engineering, economics, insurance or nance, and are often employed in modeling across the sciences. Since the lognormal is subexponential and heavy-tailed, then the asymp- totic properties of the probability that the sum goes to in nity (right tail) are typically analyzed using subexponential techniques. In contrast, the study of the asymptotics of the probability that the sum becomes very small (left tail) is a light-tailed problem and the typical tools would be saddlepoint or large deviations...
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