Criteria for large deviations

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...

Large deviations for mixtures

Suppose the distributions {μn} on Θ obey a large deviation principle (LDP) and that for each θ ∈ Θ the distributions {Pn θ } on X also obey an LDP. The main purpose of this paper is to give conditions which allow an LDP for the mixtures {Pn}, given by Pn(A) = ∫ Pn θ (A)dμn(θ), to be deduced. The treatment follows that of Dinwoodie and Zabell (1992) who, motivated by exchangeability, consider th...

Large Deviations for Langevin

We study the asymptotic behavior of asymmetrical spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the annealed law of the empirical measure on path space of these dynamics satisfy a large deviation principle in the high temperature regime. We study the rate function of this large deviation principle and prove that it achieves its minimum...

Large Deviations

0055 Large Deviations for Quicksort ∗

Let Qn be the random number of comparisons made by quicksort in sorting n distinct keys, when we assume that all n! possible orderings are equally likely. Known results concerning moments for Qn do not show how rare it is for Qn to make large deviations from its mean. Here we give a good approximation to the probability of such a large deviation, and find that this probability is quite small. A...