Related papers: Small time asymptotics for an example of strictly …
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
We consider the motion of a particle in a periodic two dimensional flow perturbed by small (molecular) diffusion. The flow is generated by a divergence free zero mean vector field. The long time behavior corresponds to the behavior of the…
Via a simulation study we compare the finite sample performance of the deconvolution kernel density estimator in the supersmooth deconvolution problem to its asymptotic behaviour predicted by two asymptotic normality theorems. Our results…
When working with asymptotically hyperbolic initial data sets for general relativity it is convenient to assume certain simplifying properties. We prove that the subset of initial data sets with such properties is dense in the set of…
The heat trace asymptotics are discussed for operators of Laplace type with Dirichlet, Robin, spectral, D/N, and transmittal boundary conditions. The heat content asymptotics are discussed for operators with time dependent coefficients and…
We derive the low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain by summing up the asymptotically dominant terms of their expansion into form factors of the quantum transfer matrix. Our…
The well-known formal analogy between time and absolute temperature, existing on the quantum level, is considered as a profound duality relationship requiring some modifications in the conventional quantum dynamics. They consist of tiny…
The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
We consider time-changed diffusions driven by generators with discontinuous coefficients. The PDE's connections are investigated and in particular some results on the asymptotic analysis according to the behaviour of the coefficients are…
We consider the heat equation associated with a class of second order hypoelliptic H\"{o}rmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a…
In the present paper, we study a model of a thermoelastic string that is initially heated. We classify all the possible asymptotic states when time tends to infinity of such a model. Actually, we show that whatever the initial data is, a…
We study the 2d directed polymer in random environment in a novel *quasi-critical regime*, which interpolates between the much studied sub-critical and critical regimes. We prove Edwards-Wilkinson fluctuations throughout the quasi-critical…
We prove duality estimates for time-fractional and more general subdiffusion problems. An important example is given by subdiffusive porous medium type equations. Our estimates can be used to prove uniqueness of weak solutions to such…
For the spherical symmetric case, all quantities describing the relaxed dark matter halo can be expressed as functions of the gravitational potential $\Phi$. Decomposing the radial velocity dispersion $\sigma_r$ with respect to $\Phi$ at…
A steady-state convection-diffusion problem with a small diffusion of order $\mathcal{O}(\varepsilon)$ is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter…
We present an asymptotic form of the Boussinesq equations in the limit of small Peclet numbers i.e. when the time scale of motions is much larger than the time scale of thermal diffusion. We find that, in this limit, the effects of thermal…
We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of…
We study the short-time asymptotical behavior of stochastic flows on \mathbb{R} in the \sup-norm. The results are stated in terms of a Gaussian process associated with the covariation of the flow. In case the Gaussian process has a…
Let $X$ be a compact oriented CR manifold of dimension $2n+1$, $n \ge 1$, with a nondegenerate Levi form of constant signature $(n_-, n_+)$. Suppose that condition $Y(q)$ holds at each point of $X$, we establish the small time asymptotics…
An asymptotic low-temperature expansion is performed for an integrable bosonic lattice model and for the critical spin-1/2 Heisenberg chain in a magnetic field. The results apply to the integrable Bose gas as well. We also comment on a…