Related papers: Renewal Theory and Geometric Infinite Divisibility

This article discusses some recent trends in Ramsey theory on infinite structures. Trees and their Ramsey theory have been vital to these investigations. The main ideas behind the author's recent method of trees with coding nodes are…

This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…

We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…

A new, conceptual proof approach for establishing the existence of regenerative space-time points for symmetric, translation invariant, finite-range interaction contact processes on survival is shown. The proof is elementary, complements…

We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for…

We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we…

We consider a heat equation and a wave equation in a spatial interval over a time interval. This article deals with inverse problems of determining sizes of spatial intervals by extra boundary data of solutions of the governing equations.…

We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…

We obtain results on mixing for a large class of (not necessarily Markov) infinite measure semiflows and flows. Erickson proved, amongst other things, a strong renewal theorem in the corresponding i.i.d. setting. Using operator renewal…

We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation.…

First, Second and Combined Laws of Thermodynamics are revised in terms of entropy change, partial entropy, partial volume, and chemical potential.

Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…

This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…

We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…

This article discusses methods of geometric analysis in general relativity, with special focus on the role of "critical surfaces" such as minimal surfaces, marginal surface, maximal surfaces and null surfaces.

The ability to estimate the rate of convergence for the distributions of regenerative processes is in great demand. These processes are often encountered in queuing theory and in related problems. In some papers on regenerative processes,…

For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…

This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…

It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…

We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence…