Related papers: Effect of Random Time Changes on Loewner Hulls
A nonequilibrium fluctuation theorem is established for a colloidal particle driven by an external force within the hydrodynamic theory of Brownian motion, describing hydrodynamic memory effects such as the t^(-3/2) power-law decay of the…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
Considering a BDI symmetric one-dimensional SSH model, we explore the fate of the bulk topological invariant, namely, the winding number under a generic time dependent perturbation; the effective Hamiltonian, that generates the temporal…
Laminar-turbulent transition on a rotating wind turbine blade at a chord Reynolds number of $1 \times 10^5$ and varying angles of attack ($AoA$) is studied with direct numerical simulations and linear stability theory. The rotation effects…
We compute a closed-form expression for the moment generating function $\hat{f}(x;\lambda,\alpha)=\frac{1}{\lambda}\mathbb{E}_x(e^{\alpha L_{\tau}})$, where $L_t$ is the local time at zero for standard Brownian motion with reflecting…
We construct a planar process that switches randomly between the flows of two linear systems built from two Hurwitz matrices (all eigenvalues have negative real parts). The goal here is to study the long time behaviour according to the…
We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium…
We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This…
We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0<x<t}. This article determines the parabolic Martin boundary and all harmonic functions associated with this process.…
We have proved in a previous paper that a space-time Brownian motion conditioned to remain in a Weyl chamber associated to an affine Kac-Moody Lie algebra is distributed as the radial part process of a Brownian sheet on the compact real…
The quantum Brownian motion of a charged particle in the electromagnetic vacuum fluctuations is investigated near a perfectly reflecting flat boundary, taking into account the smooth switching process in the measurement. Constructing a…
We disclose the origin of anisotropic percolation perimeters in terms of the Stochastic Loewner Evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multi-layered and directed…
Given a random time, we characterize the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some…
A continuous complex rotation of time $t\mapsto t\EXP{-i\theta}$ is shown to smooth out the huge fluctuations that characterise chaotic tunnelling. This is illustrated in the kicked rotor model (quantum standard map) where the period of the…
Langevin stochastic differential equations provide a dynamical description of pulsar timing noise and gravitational wave background (GWB) signals. They are also central to state space algorithms that have gained traction in pulsar timing…
A huge number of technological and biological systems involves the lubricated contact between rough surfaces of soft solids in relative accelerated motion. Examples include dynamical rubber seals and the human joints. In this study we…
When angular objects in lensing are considered as linear objects, interesting phenomena start happening. Tachyonic caustics are one example. We review that the intrinsic variables of the lens equation are angular variables. We argue that…
We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval $[0,T]$, having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the…
In this paper, we study small-time asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H\in(1/2,1)$ and magnitude $\ep^H$. By building up a…
In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its…