相关论文: mm-Spaces and group actions

In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.

These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…

We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories. We work through numerous examples to demonstrate the power of these notions. Turning to representations, which are actions that…

This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…

In this work, we give a survey of recent developments in the theory of partial actions of groups and Hopf algebras.

The phenomenon of concentration of measure on high dimensional structures is usually stated in terms of a metric space with a Borel measure, also called an mm-space. We extend some of the mm-space concepts to the setting of a quasi-metric…

These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.

Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures,…

We describe characteristic factors for certain averages arising from commuting actions of locally compact, second-countable, amenable groups. Under some ergodicity assumptions we use these factors to prove a form of multiple recurrence for…

These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.

We study periodic points and finitely supported invariant measures for continuous semigroup actions. Introducing suitable notions of periodicity in both topological and measure-theoretical contexts, we analyze the space of invariant Borel…

We present a unified theory for the almost periodicity of functions with values in an arbitrary Banach space, measures and distributions via almost periodic elements for the action of a locally compact abelian group on a uniform topological…

This lecture has the following sections: Systems and States; Brownian Motion; Segmental Relaxation and the Glass Transition; Dynamics of a Free Chain; Entanglement and Reptation. Appendices cover: Linear response theory, relaxation,…

Generalizing Block and Weinberger's characterization of amenability we introduce the notion of uniformly finite homology for a group action on a compact space and use it to give a homological characterization of topological amenability for…

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…

We perform a numerical analysis of a recent introduced model for describing collective movement in alarmed animals groups. This model, derived from a position-based interaction and a limited attention field, displays a non-equilibrium phase…

The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…

This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living,…

In this paper by using of generalized groups and their generalized actions, we define and study the notion of $T$-spaces. Moreover, we study properties of the quotient space of a $T$-space and we present the conditions that imply to the…

We introduce a topometric version of Lipschitz-free spaces and study its universal property. Another aim of this paper is to investigate actions of topological groups $G$ on Lipschitz-free spaces $\mathcal{F}(M)$, induced by isometric…