Related papers: Tightness for Thick Points in two dimensions
We investigate the convexity property on $(0,1)$ of the function $$f_a(x)=\frac{{\cal K}{(\sqrt x)}}{a-(1/2)\log(1-x)}.$$ We show that $f_a$ is strictly convex on $(0,1)$ if and only if $a\geq a_c$ and $1/f_a$ is strictly convex on $(0,1)$…
A significant asymmetry in the distribution of faint blue stars in the inner Galaxy, Quadrant 1 (l = 20 to 45 degrees) compared to Quadrant 4 was first reported by Larsen & Humphreys (1996). Parker et al (2003, 2004) greatly expanded the…
A massive rigid particle model in $(3+1)$ dimensions is reformulated in terms of twistors. Beginning with a first-order Lagrangian, we establish a twistor representation of the Lagrangian for a massive particle with rigidity. The twistorial…
We calculate analytically the probability density $P(t_m)$ of the time $t_m$ at which a continuous-time Brownian motion (with and without drift) attains its maximum before passing through the origin for the first time. We also compute the…
The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…
Consider n non-intersecting particles on the real line (Dyson Brownian motions), all starting from the origin at time=0, and forced to return to x=0 at time=1. For large n, the average mean density of particles has its support, for each…
Modelling the flow in a thin accretion disc like a dynamical system, we analyse the nature of the critical points of the steady solutions of the flow. For the simple inviscid disc there are two critical points, with the outer one being a…
We consider a Brownian particle with diffusion coefficient $D$ in a $d$-dimensional ball of radius $R$ with reflecting boundaries. We study the maximum $M_x(t)$ of the trajectory of the particle along the $x$-direction at time $t$. In the…
We have considered precession in accretion disks in which a second moment of inertia relative to an axis perpendicular to the axis of rotation may be very important. This formalism, that takes into account the precession contribution to the…
The connection between absorbing boundary conditions and hard walls is well established in the mathematical literature for a variety of stochastic models, including for instance the Brownian motion. In this paper we explore this duality for…
We show that, even for a soft collision like forward elastic scattering, the phase of the amplitude is extremely sensitive to a breakdown of strict causality in local QFT. This is especially the case when the breakdown is manifested by a…
Large-amplitude isothermal fluctuations in the dark matter energy density, parameterized by $\Phi\equiv\delta\rhodm/\rhodm$, are studied within the framework of a spherical collapse model. For $\Phi \ga 1$, a fluctuation collapses in the…
This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…
In one and two dimensions, the first-passage time for a diffusing particle in the presence of a radial potential flow to hit a sphere, conditioned on actually hitting the sphere, is independent of the sign of the drift. Moreover, the…
We study the dynamics and clustering of dust particles with inertia in shock-dominated compressible turbulence using the two-dimensional, stochastically forced Burgers equation. At small Stokes numbers, shock trapping leads to extreme…
We prove some rigidity theorems for configurations of closed disks. First, fix two collections $\mathcal{C}$ and $\tilde{\mathcal{C}}$ of closed disks in the Riemann sphere $\hat{\mathbb{C}}$, sharing a contact graph which…
An exact formula is derived, as an integral, for the mean square winding angle of Brownian motion (that is, diffusion) after time t, around an infinitely long impenetrable cylinder of radius a, having started at radius R(>a) from the axis.…
Based on the London equation, we use a rotor-free vector potential ${\bf A}$, and current measurements by a SQUID, to determine the superconducting Pearl length $\Lambda$, and coherence length $\xi$, of ultra-thin, ring shaped, MoSi films,…
A method to construct exact general relativistic thick disks that is a simple generalization of the ``displace, cut and reflect'' method commonly used in Newtonian, as well as, in Einstein theory of gravitation is presented. This…
Using three-dimensional general relativistic magnetohydrodynamic simulations with electron and proton thermodynamics and an electron cooling function, we probe the inner radial and vertical structure of weakly magnetized geometrically thin…