Related papers: Extreme events for horocycle flows
Uniform shear flow is a paradigmatic example of a nonequilibrium fluid state exhibiting non-Newtonian behavior. It is characterized by uniform density and temperature and a linear velocity profile $U_x(y)=a y$, where $a$ is the constant…
A recent paper of Tsai shows how the first few moments of a stochastic flow in the space of measures can completely determine its law. Here we give another proof of this result for the particular case of the one-dimensional multiplicative…
We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a…
We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes…
In recent work of Luo and Hou, a new scenario for finite time blow up in solutions of 3D Euler equation has been proposed. The scenario involves a ring of hyperbolic points of the flow located at the boundary of a cylinder. In this paper,…
Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)$, for $t\in [0,T)$. In…
We study analytically, via the Newman-Penrose formalism, the late time decay of scalar, electromagnetic, and gravitational perturbations outside a realistic rotating (Kerr) black hole. We find a power-law decay at timelike infinity, as well…
We propose that fast scrambling on finite-entropy stretched horizons can be modeled by a diffusion process on an effective ultrametric geometry. A scrambling time scaling logarithmically with the entropy is obtained when the elementary…
We examine a steepest energy descent flow with obstacle constraint in higher order energy frameworks where the maximum principle is not available. We construct the flow under general assumptions using De Giorgi's minimizing movement scheme.…
We study the distributions of event-time returns and clock-time returns at different microscopic timescales using ultra-high-frequency data extracted from the limit-order books of 23 stocks traded in the Chinese stock market in 2003. We…
This article deals with limit theorems for certain loop variables for loop soups whose intensity approaches infinity. We first consider random walk loop soups on finite graphs and obtain a central limit theorem when the loop variable is the…
The curve shortening flow is a geometric heat equation for curves and provides an accessible setting to illustrate many important concepts from nonlinear partial differential equations, including maximum principle estimates, monotonicity…
Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…
In event by event hydrodynamic model, we have simulated 30-40\% Au+Au collisions at RHIC and computed the slope parameter from the invariant pion distribution. In each event, the slope parameter fluctuates azimuthally. Fourier expansion…
Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal…
We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $\alpha+1$, where $\alpha \in (1,2)$. The limiting components are…
We obtain a description of the Poincar\'e recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by…
We found the precise condition for the decay as $t\to\infty$ of Besicovitch almost periodic entropy solutions of multidimensional scalar conservation laws. Moreover, in the case of one space variable we establish asymptotic convergence of…
The paper studies a curvature flow linked to the physical phenomenon of wound closure. Under the flow we show that a closed, initially convex or close-to-convex curve shrinks to a round point in finite time. We also study the singularity,…
Rainfall exhibits extreme variability at many space and time scales and calls for a statistical description. Based on an analysis of radar measurements of precipitation over the tropical oceans, we introduce a new probability law for the…