相关论文: On $ h $-transforms of one-dimensional diffusions …

In this paper the interface between two transformation media or between a transformation medium and vacuum is studied. Strictly from the transformation optics point of view the consequences of the boundary conditions at such interfaces are…

While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…

We study the initial-boundary value problem for the Hamilton-Jacobi equation with nonlinear diffusion $u_t=\Delta_p u+|\nabla u|^q$ in a two-dimensional domain for $q>p>2$. It is known that the spatial derivative of solutions may become…

For diffusion-reaction equations employing a splitting procedure is attractive as it reduces the computational demand and facilitates a parallel implementation. Moreover, it opens up the possibility to construct second-order integrators…

We deal with heteroclinic planar fronts for parameter-dependent reaction-diffusion equations with bistable reaction and saturating diffusive term like $$ u_t=\epsilon \, \textrm{div}\, \left(\frac{\nabla u}{\sqrt{1+\vert \nabla u…

It is well known that index (discrete-time)-limited sampled sequences leak outside the support set when a band-limiting operation is applied. Similarly, a fractional shift causes an index-limited sequence to be infinite in extent due to the…

We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution…

We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of…

An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…

We discover that a class of bubbles of nothing are embedded as time dependent scaling limits of previous spacelike-brane solutions. With the right initial conditions, a near-bubble solution can relax its expansion and open the compact…

A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…

We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d1 ~ 26 and…

The extraordinary transition which occurs in the two-dimensional O(n) model for $n<1$ at sufficiently enhanced surface couplings is studied by conformal perturbation theory about infinite coupling and by finite-size scaling of the spectrum…

It is known that diffusion provokes substantial changes in continuous absorbing phase transitions. Conversely, its effect on discontinuous transitions is much less understood. In order to shed light in this direction, we study the inclusion…

We derive a singular diffusion limit for the position of a tagged particle in zero range interacting particle processes on a one dimensional torus with a Sinai-type random environment via two steps. In the first step, a regularization is…

We consider the inclusion process on the complete graph with vanishing diffusivity, which leads to condensation of particles in the thermodynamic limit. Describing particle configurations in terms of size-biased and appropriately scaled…

When the unconditioned process is a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, the local time $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ at the origin $x=0$ is one of the most important time-additive…

Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…

We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…