Related papers: The variance of the shock in the HAD process
An exponential horn geometry is introduced in order to establish cellular detonations with a constant mean lateral mass divergence, propagating at quasi-steady speeds below the Chapman-Jouguet value. Experiments and simulations demonstrated…
We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by $a\geq0$, which creates a shock in the particle density of order $aT^{-1/3},$ $T$ the observation time. When starting from step initial data,…
Hawkes processes were first introduced to obtain microscopic models for the rough volatility observed in asset prices. Scaling limits of such processes leads to the rough-Heston model that describes the macroscopic behavior. Blanc et al.…
This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…
We investigate the spatial distribution of aftershocks and we find that aftershock linear density exhibits a maximum, that depends on the mainshock magnitude, followed by a power law decay. The exponent controlling the asymptotic decay and…
Let $Z$ be a random variable with values in a proper closed convex cone $C\subset \mathbb{R}^d$, $A$ a random endomorphism of $C$ and $N$ a random integer. We assume that $Z$, $A$, $N$ are independent. Given $N$ independent copies…
We prove that the variance of the current across a characteristic is of order t^{2/3} in a stationary asymmetric simple exclusion process, and that the diffusivity has order t^{1/3}. The proof proceeds via couplings to show the…
Using microscopic price models based on Hawkes processes, it has been shown that under some no-arbitrage condition, the high degree of endogeneity of markets together with the phenomenon of metaorders splitting generate rough Heston-type…
Using a time-dependent multifluid, magnetohydrodynamic code, we calculated the structure of steady perpendicular and oblique C-type shocks in dusty plasmas. We included relevant processes to describe mass transfer between the different…
Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma^2_{\rho/\rho_0}$, is of…
The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different…
We consider sequences $(X_t^N)_{t\geq0}$ of Markov processes in two dimensions whose fluid limit is a stable solution of an ordinary differential equation of the form $\dot{x}_t=b(x_t)$, where $b(x)={\pmatrix{-\mu 0 0 \lambda}}x+\tau(x)$…
We prove a central limit type theorem for critical marked Hawkes processes. We study the case where the marks are i.i.d. with nonnegative values and their common distribution is either heavy tailed or has finite variance. The kernel…
The paper presents a method for solving hydraulic fracture problems accounting for the lag. The method consists in matching the outer (basic) solution neglecting the lag, with the inner (auxiliary) solution of the derived 1D integral…
We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at…
Using the bottom-up approach in a holographic setting, we attempt to study both the transport and thermodynamic properties of a generic system in 3+1 dimensional bulk spacetime. We show the exact 1/T and $T^2$ dependence of the longitudinal…
The tacnode process is a universal determinantal point process arising from non-intersecting particle systems and tiling problems. It is the aim of this work to explore the integrable structure and large gap asymptotics for the gap…
In recent years, the behavior of dislocations in random solid solutions has received renewed interest, and several models have been discussed where random alloys are treated as effective media containing random distributions of dilatation…
Mott variable range hopping is a fundamental mechanism for low-temperature electron conduction in disordered solids in the regime of Anderson localization. In a mean field approximation, it reduces to a random walk (shortly, Mott random…
We prove large deviation principles (LDP) for the invariant measures of the multiclass totally asymmetric simple exclusion process (TASEP) and the multiclass Hammersely-Aldous-Diaconis (HAD) process on a torus. The proof is based on a…