227 research outputs found
Wetting of gradient fields: pathwise estimates
We consider the wetting transition in the framework of an effective interface
model of gradient type, in dimension 2 and higher. We prove pathwise estimates
showing that the interface is localized in the whole thermodynamically-defined
partial wetting regime considered in earlier works. Moreover, we study how the
interface delocalizes as the wetting transition is approached. Our main tool is
reflection positivity in the form of the chessboard estimate.Comment: Some typos removed after proofreading. Version to be published in
PTR
Fluctuations for the Ginzburg-Landau Interface Model on a Bounded Domain
We study the massless field on , where is a bounded domain with smooth boundary, with Hamiltonian
\CH(h) = \sum_{x \sim y} \CV(h(x) - h(y)). The interaction \CV is assumed
to be symmetric and uniformly convex. This is a general model for a
-dimensional effective interface where represents the height. We
take our boundary conditions to be a continuous perturbation of a macroscopic
tilt: for , , and
continuous. We prove that the fluctuations of linear
functionals of about the tilt converge in the limit to a Gaussian free
field on , the standard Gaussian with respect to the weighted Dirichlet
inner product for some explicit . In a subsequent article,
we will employ the tools developed here to resolve a conjecture of Sheffield
that the zero contour lines of are asymptotically described by , a
conformally invariant random curve.Comment: 58 page
Pathwise McKean-Vlasov Theory with Additive Noise
Abstract. We take a pathwise approach to classical McKean-Vlasov stochastic
differential equations with additive noise, as e.g. exposed in Sznitmann [38].
Our study was prompted by some concrete problems in battery modelling [23], and
also by recent progrss on rough-pathwise McKean-Vlasov theory, notably
Cass-Lyons [10], and then Bailleul, Catellier and Delarue [4]. Such a "pathwise
McKean-Vlasov theory" can be traced back to Tanaka [40]. This paper can be seen
as an attempt to advertize the ideas, power and simplicity of the pathwise
appproach, not so easily extracted from [4, 10, 40], together with a number of
novel applications. These include mean field convergence without a priori
independence and exchangeability assumption; common noise, c\ue0dl\ue0g noise,
and reflecting boundaries. Last not least, we generalize Dawson-G\ue4rtner large
deviations and the central limit theorem to a non-Brownian noise setting
Minimum entropy production principle from a dynamical fluctuation law
The minimum entropy production principle provides an approximative
variational characterization of close-to-equilibrium stationary states, both
for macroscopic systems and for stochastic models. Analyzing the fluctuations
of the empirical distribution of occupation times for a class of Markov
processes, we identify the entropy production as the large deviation rate
function, up to leading order when expanding around a detailed balance
dynamics. In that way, the minimum entropy production principle is recognized
as a consequence of the structure of dynamical fluctuations, and its
approximate character gets an explanation. We also discuss the subtlety
emerging when applying the principle to systems whose degrees of freedom change
sign under kinematical time-reversal.Comment: 17 page
Analysis of airplane boarding via space-time geometry and random matrix theory
We show that airplane boarding can be asymptotically modeled by 2-dimensional
Lorentzian geometry. Boarding time is given by the maximal proper time among
curves in the model. Discrepancies between the model and simulation results are
closely related to random matrix theory. We then show how such models can be
used to explain why some commonly practiced airline boarding policies are
ineffective and even detrimental.Comment: 4 page
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