Related papers: Polymer Measure: Varadhan's Renormalization Revisi…
A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
The paper is devoted to the study of a parametric deformation model of independent and identically random variables. Firstly, we construct an efficient and very easy to compute recursive estimate of the parameter. Our stochastic estimator…
The systematic expansion method of the solution of the Fokker-Planck equation is developed by generalizing the formulation proposed in [J. Phys. A50, 325001 (2017)]. Using this method, we obtain a new formula to calculate the mean work…
We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the…
At fast timescales, the self-similarity of random Brownian motion is expected to break down and be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation…
We study the mixing properties of a Brownian motion whose movements are hindered by semipermeable barriers. Our setting assumes that the process takes values in a smooth planar domain and that the barriers are one-dimensional closed curves.…
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1 -minimization algorithm, originally proposed in the context…
This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time $T$, considering the…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
In this paper we consider the problem of recovering the conformal factor in a conformal class of Riemannian metrics from the boundary measurement of one wave field. More precisely, using boundary control operators, we derive an explicit…
We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…
We extend the ideas of (Barbour 1990) and use Stein's method to obtain a bound on the distance between a scaled time-changed random walk and a time-changed Brownian Motion. We then apply this result to bound the distance between a…
We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel…
We describe a novel algorithm for rounding packing integer programs based on multidimensional Brownian motion in $\mathbb{R}^n$. Starting from an optimal fractional feasible solution $\bar{x}$, the procedure converges in polynomial time to…
We analyze the rectified motion of a Brownian particle in a confined environment. We show the emergence of strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by…
We prove a representation for the average wave function of the Schr\"odinger equation with a white noise potential in $d=1,2$, in terms of the renormalized self-intersection local time of a Brownian motion.
In a recent paper, a new parametrization for the dark matter (DM) speed distribution f(v) was proposed for use in the analysis of data from direct detection experiments. This parametrization involves expressing the logarithm of the speed…
Based on Brownian dynamics simulations we study the collective behavior of a twodimensional system of repulsively interacting colloidal particles, where each particle is propelled by a repulsive feedback force with time delay $\tau$.…
The original density is 1 for $t\in (0,1)$, $b$ is an integer base ($b\geq 2$%), and $p\in (0,1)$ is a parameter. The first construction stage divides the unit interval into $b$ subintervals and multiplies the density in each subinterval by…