Dresden 2014 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 34: Symposium SYGP: Stochastic Dynamics of Growth Processes in Biological and Social Systems

DY 34.1: Hauptvortrag

Donnerstag, 3. April 2014, 15:00–15:30, HSZ 02

Noisy invasions: large fluctuations in stochastic invasion models — •Baruch Meerson — Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 Israel

Invasion fronts have been recognized as important, and often fateful, phenomena in ecology, epidemiology and biological evolution. The position of an invasion front fluctuates because of the shot noise of individual reactions. What is the probability to observe, at a given time, a front displacement that is considerably smaller or larger than that predicted from deterministic theory? The answer strongly depends on whether the front propagates into a metastable or unstable state, and I will review recent theoretical progress in both cases. The progress is mostly based on a dissipative version of WKB theory which assumes many individuals in the front region. In this theory the most likely history of the system, for a given front displacement, is encoded in a special trajectory of the underlying effective Hamilton mechanics, a classical field theory. This special trajectory is described by a traveling front solution. For fronts, propagating into unstable states, very large front displacements are much more likely than very small ones. The leading contribution to the probability density of a large displacement comes from a few fastest particles running ahead of the front. For such fronts the WKB theory breaks down, and new methods are needed.