Baruch Meerson (Racah Institute of Physics, Hebrew University of Jerusalem)
Abstract. Extinction of a long-lived self-regulating population is a dramatic effect. It can result from a rare large fluctuation coming from the discreteness of individuals and stochasticity of their births, deaths and interactions. It also epitomizes the importance of rare events. Predicting the mean time to extinction accurately is important in many applications. Examples include assessment of viability of small populations and evaluation of the lifetime of an infectious disease in a closed community. I will show how one can use a variant of WKB approximation, which originates in quantum mechanics and other areas of physics, to evaluate the mean time to extinction of a stochastic population. In the WKB framework the most likely path of the population to extinction is described by a special trajectory of an underlying classical Hamiltonian system.