Related papers: Heat content for Gaussian processes: small-time as…

Transition to thermal equilibrium in a uniformly heated two-dimensional harmonic triangular lattice with nearest neighbor interactions is investigated. Initial conditions, typical for molecular dynamics simulations, are considered.…

In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is…

Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…

We study the asymptotic behaviour of solutions of a class of linear non-local measure-valued differential equations with time delay. Our main result states that the solutions asymptotically exhibit a parabolic like behaviour in the large…

In this work we study the large-time behaviour of solutions of the Heat Equation in the hyperbolic space $\mathbb{H}^d$, providing precise speeds of convergence in $L^1$ and $L^\infty$ to their asymptotic profiles by means of an adaptation…

We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing diffusivity. Such diffusion processes arise…

The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…

Sub-Gaussian and subexponential distributions are introduced and applied to study the fluctuation-response relation out of equilibrium. A bound on the difference in expected values of an arbitrary sub-Gaussian or subexponential physical…

We define Gaussian assignment process, determine the asymptotic behavior of its maximum's expectation and suggest an explicit strategy that attains the corresponding asymptotics.

It is shown that the timelike asymptotic properties of thermal correlation functions in relativistic quantum field theory can consistently be described in terms of free fields carrying some stochastic degree of freedom which couples to the…

Let (M,g) be a compact Riemannian manifold without boundary. Let D be a compact subdomain of M with smooth boundary. We examine the heat content asymptotics for the heat flow from D into M where both the initial temperature and the specific…

Let $(M^n, g)$ be a complete Riemannian manifold with $Rc\geq -Kg$, $H(x, y, t)$ is the heat kernel on $M^n$, and $H= (4\pi t)^{-\frac{n}{2}}e^{-f}$. Nash entropy is defined as $N(H, t)= \int_{M^n} (fH) d\mu(x)- \frac{n}{2}$. We studied the…

In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in $\mathbb{R}^N$. Different homogeneous boundary conditions are…

Using the framework of stochastic thermodynamics we study heat production related to the stochastic motion of a particle driven by repulsive, nonlinear, time-delayed feedback. Recently it has been shown that this type of feedback can lead…

Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…

We consider the statistical linear inverse problem of recovering the unknown initial heat state from noisy interior measurements over an inhomogeneous domain of the solution to the heat equation at a fixed time instant. We employ…

We consider the Cauchy problem for the generalized Fornberg-Whitham equation with dissipation. This is one of the nonlinear, nonlocal and dispersive-dissipative equations. The main topic of this paper is an asymptotic analysis for the…

We consider the solution of $u_t-\Delta^G_p u=0$ in a (not necessarily bounded) domain, satisfying $u=0$ initially and $u=1$ on the boundary at all times. Here, $\Delta^G_p u$ is the game-theoretic or normalized $p$-laplacian. We derive new…

We study the stochastic heat flow with constant initial data and analyze its spatial average on the scale of $\varepsilon\ll1$. We prove that the logarithm of the averaged process satisfies a pointwise central limit theorem: After being…

We derive the asymptotic behavior for an additive functional of two independent self-similar Gaussian processes when their intersection local time exists, using the method of moments.