Related papers: The Martin Boundary of the Young-Fibonacci Lattice
The t-Martin boundary of a random walk on a half-space with reflected boundary conditions is identified. It is shown in particular that the t-Martin boundary of such a random walk is not stable in the following sense : for different values…
Given a probability measure on a finitely generated group, its Martin boundary is a natural way to compactify the group using the Green function of the corresponding random walk. For finitely supported measures in hyperbolic groups, it is…
It is shown that the operator space generated by peripheral eigenvectors of a unital completely positive map on a von Neumann algebra has a $C^*$-algebra structure. This extends the notion of non-commutative Poisson boundary by including…
In this paper, new probability bounds are derived for algebraic lattice codes. This is done by using the Dedekind zeta functions of the algebraic number fields involved in the lattice constructions. In particular, it is shown how to upper…
We give conditions under which nonuniformly expanding maps exhibit lower bounds of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequality for the transfer…
The lattice sine-Gordon equation is an integrable partial difference equation on ${\mathbb Z}^2$, which approaches the sine-Gordon equation in a continuum limit. In this paper, we show that the non-autonomous lattice sine-Gordon equation…
The dynamics of finite nonperiodic Toda lattice is an isospectral deformation of the finite three--diagonal Jacobi matrix. It is known since the work of Stieltjes that such matrices are in one--to--one correspondence with their Weyl…
We determine the asymptotic behavior of the Green function for zero-drift random walks confined to multidimensional convex cones. As a consequence, we prove that there is a unique positive discrete harmonic function for these processes (up…
An intuitive probabilistic alternative for the construction of the Martin boundary is presented along with a construction of maximal representing measures for positive harmonic functions.
We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional…
Certain mathematical structures make a habit of reoccuring in the most diverse list of settings. Some obvious examples exhibiting this intrusive type of behavior include the Fibonacci numbers, the Catalan numbers, the quaternions, and the…
We study a problem with three equivalent formulations: describing Gibbs measures for five-vertex model in quadrant; classifying coherent systems on a p-deformation of the Gelfand-Tsetlin graph related to Grothendieck polynomials; finding…
We study resonances for Jacobi operators on the half lattice with matrix valued coefficient and finitely supported perturbations. We describe a forbidden domain, the geometry of resonances and their asymptotics when the main coefficient of…
We consider killed planar random walks on isoradial graphs. Contrary to the lattice case, isoradial graphs are not translation invariant, do not admit any group structure and are spatially non-homogeneous. Despite these crucial differences,…
We provide a geometric representation of the Poisson and Martin boundaries of a transient, bounded degree triangulation of the plane in terms of its circle packing in the unit disc. (This packing is unique up to M\"obius transformations.)…
New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting…
Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…
We consider a class of infinite weighted metric trees obtained as perturbations of self-similar regular trees. Possible definitions of the boundary traces of functions in the Sobolev space on such a structure are discussed by using…
We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the…
The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching a compact surface (interface). The lower-dimensional piece is a so-called…