相关论文: Tiny fluctuations of the averaging process around …
We prove that the equilibrium fluctuations of the symmetric simple exclusion process in contact with slow boundaries is given by an Ornstein-Uhlenbeck process with Dirichlet, Robin or Neumann boundary conditions depending on the range of…
We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…
Cavity point-to-set correlations are real-space tools to detect the roughening of the free-energy landscape that accompanies the dynamical slowdown of glass-forming liquids. Measuring these correlations in model glass formers remains,…
Asymptotically large Reynolds number hydrodynamic turbulence is characterized by multi-scaling of moments of velocity increments and spatial derivatives. With decreasing Reynolds number toward $R_{\lambda}=R^{tr}_{\lambda}\approx 9.0$, the…
In this paper, we present a fluctuation analysis of a type of parabolic equations with large, highly oscillatory, random potentials around the homogenization limit. With a Feynman-Kac representation, the Kipnis-Varadhan's method, and a…
We consider the Cahn-Hilliard equation in one space dimension, perturbed by the derivative of a space and time white noise of intensity $\epsilon^{\frac 12}$, and we investigate the effect of the noise, as $\epsilon \to 0$, on the solutions…
We study the fluctuations of the area $A(t)= \int_0^t x(\tau)\, d\tau$ under a self-similar Gaussian process (SGP) $x(\tau)$ with Hurst exponent $H>0$ (e.g., standard or fractional Brownian motion, or the random acceleration process) that…
We consider the discrete directed polymer model with i.i.d. environment and we study the fluctuations of the tail $n^{(d-2)/4}(W_\infty - W_n)$ of the normalized partition function. It was proven by Comets and Liu, that for sufficiently…
In light of recent advances in time-step independent stochastic integrators for Langevin equations, we revisit the considerations for using non-Gaussian distributions for the thermal noise term in discrete-time thermostats. We find that the…
We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium…
A special type of geometric situation in ensembles of non-intersecting paths occurs when the non-intersecting trajectories are required to be nonnegative so that the limit shape becomes tangential to the hard-edge $0$. The local fluctuation…
We provide a method for calculating time-averaged stress fluctuations on surfaces in a viscous incompressible fluid at equilibrium. We assume that (i) the time-averaged fluctuating stress is balanced in equilibrium at each position and that…
Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as noise, hold the…
This thesis deals with the investigation of a H(div)-conforming hybrid discontinuous Galerkin discretization for incompressible turbulent flows. The discretization method provides many physical and solving-oriented properties, which may be…
Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random…
The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and…
Characterizing current fluctuations in a steady state is of fundamental interest and has attracted considerable attention in the recent past. However, the bulk of the studies are limited to systems that either do not exhibit a phase…
Differential rotation is known to suppress linear instabilities in fusion plasmas. However, even in the absence of growing eigenmodes, subcritical fluctuations that grow transiently can lead to sustained turbulence. Here transient growth of…
We study current fluctuations in a one-dimensional interacting particle system known as the dual smoothing process that is dual to random motions in a Howitt-Warren flow. The Howitt-Warren flow can be regarded as the transition kernels of a…
We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a non-equilibrium quantum system with a critical point phase-transition, that is also known to exhibit…