Large deviations and equilibrium selection in large populations

Large deviations and equilibrium selection in large populations

This paper uses the theory of large deviations to analyse equilibrium selection in one-dimensional games with large populations where the system evolves according to a jump Markov process. The equilibria selected maximise a quasi-potential function which can be determined by solving a polynomial equation. Estimates of waiting times are also given. It shows that the equilibria about which there ...

Large Deviations for Large Capacity

In this paper, we study large deviations of large capacity loss networks with xed routing. We use two-level modelling for the loss networks: the call level and the cell level. At the call level, a call request is accepted if it succeeds an admission test. The test is based on a polyhedral set of the number of calls in progress when a new call arrives. After being accepted, a call then transmits...

WKB theory of large deviations in stochastic populations

Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics – such as those determining population extinction, fixation or switching between different states...

Large Deviations

Large Deviations

This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations. 1. Large deviations for sums. The role of " large deviations " is best understood through an example. Suppose that X random variables, for instance, normally distributed with mean zero and variance 1. Then, E e θ(X 1 +···+X n) = E[e θX ...