Large deviations formalism for multifractals

Thermodynamic Formalism, Large Deviation, and Multifractals

Nonconcave Entropies in Multifractals and the Thermodynamic Formalism

We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy function yields the correct multifractal spectrum only when the latter is wholly concave. If the spectrum has no definite concavity, then the transform yield...

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...