Related papers: Moderate Deviations for a Curie-Weiss model with d…
The control of bipedal robotic walking remains a challenging problem in the domains of computation and experiment, due to the multi-body dynamics and various sources of uncertainty. In recent years, there has been a rising trend towards…
While the dynamics of dimers and polymer chains in a viscous solvent is well understood within the celebrated Rouse model, the effect of an external magnetic field on the dynamics of a charged chain is much less understood. Here we…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
Interaction of magnetic moment of point particles with external electromagnetic fields experiences unresolved theoretical and experimental discrepancies. In this work we point out several issues within the relativistic quantum mechanics and…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
Cluster Dynamical Mean Field Theories are analyzed in terms of their semiclassical limit and their causality properties, and a translation invariant formulation of the cellular dynamical mean field theory, PCDMFT, is presented. The…
Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee's approach to discrete mechanics and the difference…
We propose a new multi-dimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multi-dimensional Dirac equation, which can be further mapped to the Schr\"{o}dinger equation. We show in two ways that our DTQW is…
In this paper we establish a moderate deviation principle of the hitting times for trajectories of sums of independent and identically distributed random variables. The main idea of proof is to convert the moderate deviations over a small…
Quantum random walks are constructed on operator spaces with the aid of matrix-space lifting, a type of ampliation intermediate between those provided by spatial and ultraweak tensor products. Using a form of Wiener-Ito decomposition, a…
Let $(\xi_i,\mathcal{F}_i)_{i\geq1}$ be a sequence of martingale differences. Set $X_n=\sum_{i=1}^n \xi_i $ and $ \langle X \rangle_n=\sum_{i=1}^n \mathbf{E}(\xi_i^2|\mathcal{F}_{i-1}).$ We prove Cram\'er's moderate deviation expansions for…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
The mean field theory, in its different hues, form one of the most useful tools for calculating the single-body physical properties of a many-body system. It provides important information, like critical exponents, of the systems that do…
In this paper, we establish a moderate deviations principle for the Langevin dynamics with strong damping. The weak convergence approach plays an important role in the proof.
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…
The dynamical discrete web (DyDW),introduced in recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter \tau. The evolution is by…
We study the dynamics of a generalization of quantum coin walk on the line which is a natural model for a diffusion modified by quantum or interference effects. In particular, our results provide surprisingly simple explanations to…
The purpose of this paper is to analyze how the disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a…
In this paper, we find a natural four dimensional analog of the moderate deviation results for the capacity of the random walk, which corresponds to Bass, Chen and Rosen \cite{BCR} concerning the volume of the random walk range for $d=2$.…
We generalize a microscopic master equation method to study the dissipation dynamics of Jaynes-Cummings two-level system with a weak external driving. Using perturbative analysis to extend the damping bases theory, we derive the corrected…