Exponential asymptotics for time–space Hamiltonians

Exponential Asymptotics

Asymptotics of Exponential Families

if we use the convention that additive terms that do not contain the parameter may be dropped from log likelihoods (because they do not affect any likelihood-based statistical inferences). Thus we have another definition of exponential families: a statistical model is an exponential family of distributions if there exists a statistic Y and a parameter θ such that the log likelihood has the form...

Exponential Asymptotics for Thin Film Rupture

The formation of singularities in models of many physical systems can be described using self-similar solutions. One particular example is the finite-time rupture of a thin film of viscous fluid which coats a solid substrate. Previous studies have suggested the existence of a discrete, countably infinite number of distinct solutions of the nonlinear differential equation which describes the sel...

Asymptotics for Sparse Exponential Random Graph Models

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain a variational principle for the limiting free energy, an associated concentration of measure, the asymptotics for the mean and variance of the limiting probability distribution, and phase transitions in the edge-triangle model. Similar analysis is...

Lifshitz Asymptotics for Hamiltonians Monotone in the Randomness

This is a note for the report on the Oberwolfach Mini-Workshop: Multiscale and Variational Methods in Material Science and Quantum Theory of Solids, published in [MW]. In various aspects of the spectral analysis of random Schrödinger operators monotonicity with respect to the randomness plays a key role. In particular, both the continuity properties and the low energy behaviour of the integrate...