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Stein’s method in high dimensions with applications

Adrian Röllin (2013)

Annales de l'I.H.P. Probabilités et statistiques

Let h be a three times partially differentiable function on ℝ n , let X = ( X 1 , ... , X n ) be a collection of real-valued random variables and let Z = ( Z 1 , ... , Z n ) be a multivariate Gaussian vector. In this article, we develop Stein’s method to give error bounds on the difference 𝔼 h ( X ) - 𝔼 h ( Z ) in cases where the coordinates of X are not necessarily independent, focusing on the high dimensional case n → ∞ . In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy,...

Stimuli-Responsive Polymers in Nanotechnology: Deposition and Possible Effect on Drug Release

A. L. Yarin (2008)

Mathematical Modelling of Natural Phenomena

Stimuli-responsive polymers result in on-demand regulation of properties and functioning of various nanoscale systems. In particular, they allow stimuli-responsive control of flow rates through membranes and nanofluidic devices with submicron channel sizes. They also allow regulation of drug release from nanoparticles and nanofibers in response to temperature or pH variation in the surrounding medium. In the present work two relevant mathematical models are introduced to address precipitation-driven...

Stochastic approximations of the solution of a full Boltzmann equation with small initial data

Sylvie Meleard (2010)

ESAIM: Probability and Statistics

This paper gives an approximation of the solution of the Boltzmann equation by stochastic interacting particle systems in a case of cut-off collision operator and small initial data. In this case, following the ideas of Mischler and Perthame, we prove the existence and uniqueness of the solution of this equation and also the existence and uniqueness of the solution of the associated nonlinear martingale problem. 
Then, we first delocalize the interaction by considering a mollified Boltzmann...

Stochastic differential inclusions of Langevin type on Riemannian manifolds

Yuri E. Gliklikh, Andrei V. Obukhovskiĭ (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.

Stochastic Dynamics of Quantum Spin Systems

Adam Majewski, Robert Olkiewicz, Bogusław Zegarliński (1998)

Banach Center Publications

We show that recently introduced noncommutative L p -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.

Stochastic foundations of the universal dielectric response

Agnieszka Jurlewicz (2003)

Applicationes Mathematicae

We present a probabilistic model of the microscopic scenario of dielectric relaxation. We prove a limit theorem for random sums of a special type that appear in the model. By means of the theorem, we show that the presented approach to relaxation phenomena leads to the well known Havriliak-Negami empirical dielectric response provided the physical quantities in the relaxation scheme have heavy-tailed distributions. The mathematical model, presented here in the context of dielectric relaxation, can...

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Cipriano, F., Ouerdiane, H., Vilela Mendes, R. (2009)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 76M35, 82B31A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes.

Strong diamagnetism for general domains and application

Soeren Fournais, Bernard Helffer (2007)

Annales de l’institut Fourier

We consider the Neumann Laplacian with constant magnetic field on a regular domain in ℝ 2 . Let B be the strength of the magnetic field and let λ 1 ( B ) be the first eigenvalue of this Laplacian. It is proved that B ↦ λ 1 ( B ) is monotone increasing for large B . Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 superconductors.

Strong disorder in semidirected random polymers

N. Zygouras (2013)

Annales de l'I.H.P. Probabilités et statistiques

We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.

Study of a three component Cahn-Hilliard flow model

Franck Boyer, Céline Lapuerta (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency...

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