Related papers: Elliptic dynamical reflection algebra and partitio…
We give a Dirichlet form approach for the construction of a distorted Brownian motion in $E := [0;\infty)^n$, $n\in\mathbb{N}$, where the behavior on the boundary is determined by the competing effects of reflection from and pinning at the…
We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…
In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations with stochastic Lipschitz coefficient. We derive the existence and uniqueness of the solutions for those equations via Snell…
Electromagnetic waves in a system with a space and time dependent boundary experience both diffraction and Doppler-like frequency conversion. In order to analyse such situations, conventional methods call for either the eigenmodes or the…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we…
We consider the problem of construction of determinant formulas for the partition function of the six-vertex model with domain wall boundary conditions. In pioneering works of Korepin and Izergin a determinant formula was proposed and…
We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space-time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the…
We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain…
We consider the reflection equation algebra for a finite dimensional R-matrix for the $(h,w)$-deformed Heisenberg algebra ${\cal U}_{h,w}(h(4))$. A representation of the reflection matrix $K$ is constructed using the matrix generators…
Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra. We give a combinatorial description of Sklyanin…
We consider reflected backward stochastic differential equations with two optional barriers of class (D) satisfying Mokobodzki's separation condition and coefficient which is only continuous and non-increasing. We assume that data are…
We present simple assumptions on the constraints defining a hard core dynamics for the associated reflected stochastic differential equation to have a unique strong solution. Time-reversibility is proven for gradient systems with normal…
In this letter we show the partition function of the 8VSOS model with domain-wall boundaries satisfies the same type of functional equations as its six-vertex model counterpart. We then use these refined functional equations to obtain novel…
We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and…
This work introduces the extended Skorokhod problem (ESP) and associated extended Skorokhod map (ESM) that enable a pathwise construction of reflected diffusions that are not necessarily semimartingales. Roughly speaking, given the closure…
Optics naturally provides us with some powerful mathematical operations. Here we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be…
In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…
Point-to-point reflection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more general elliptic equations. We develop a non-local,…
We define a generalized finite element method for the discretization of elliptic partial differential equations in heterogeneous media. An adaptive local finite element basis (AL basis) on a coarse mesh which does not resolve the matrix of…