Related papers: Dynamical characterization of combinatorially rich…

We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…

The class of exact transferable utility coalitional games, introduced in 1972 by Schmeidler, has been studied both in the context of game theory and in the context of imprecise probabilities. We characterize the cone of exact games by…

We provide a comprehensive development of the basics of descriptive set theory for non-separable complete metric spaces whose weight is a singular cardinal $\lambda$ of countable confinality. Somewhat unexpectedly, the resulting theory is…

A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…

Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…

In [3] S. J. Bhatt and H. V. Dedania exposed certain classes of Banach algebras in which every element is a topological divisor of zero. We identify a new (large) class of Banach algebras with the aforementioned property, namely, the class…

In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…

We develop a dynamical version of some of the theory surrounding the Toms-Winter conjecture for simple separable nuclear C*-algebras and study its connections to the C*-algebra side via the crossed product. We introduce an analogue of…

We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular…

We show that the following are consistent with ZFC: 1. Strongly meager sets form an ideal with the same additivity as the ideal of meager sets. 2. There exists a strong measure zero set of size > d (dominating number).

We develop a new technique that allows us to show in a unified way that many well-known combinatorial theorems, including Tur\'an's theorem, Szemer\'edi's theorem and Ramsey's theorem, hold almost surely inside sparse random sets. For…

Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Monadically stable classes, originating from model theory,…

We algebraically characterize free by cyclic groups that have coarse medians, and prove that this is equivalent to the a priori stronger properties of being colourable hierarchically hyperbolic groups and being quasi-isometric to CAT(0)…

In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized…

The one-dimensional half-filled Hubbard model is considered at zero temperature within the cellular dynamical mean-field theory (CDMFT). By the computation of the spectral gap and the energy density with various cluster and bath sizes we…

Some of the classical results of Ramsey Theory can be naturally stated in terms of image partition regularity of matrices. There have been many significant results of image partition regular matrices as well as image partition regular…

We generalize the concept of divergence of finitely generated groups by introducing the upper and lower relative divergence of a finitely generated group with respect to a subgroup. Upper relative divergence generalizes Gersten's notion of…

Some filter relative notions of size, $\left( \mathcal{F},\mathcal{G}\right) $-syndeticity and piecewise $\mathcal{F} $-syndeticity, were defined and applied with clarity and focus by Shuungula, Zelenyuk and Zelenyuk in their paper ``The…

For a certain parametrized family of maps on the circle, with critical points and logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed in [19], corresponding to maps which…

This is a survey paper concerned with strongly continuous semigroups in a Banach algebra (often itself simply the algebra of bounded linear operators on a Banach space). These are defined either on $(0,\infty)$ or on a sector in the complex…