(2024/01/30-2024/12/31)
2024/11/22, 10:00 a.m., Tencent Meeting
Tang Dingxuan (Northwest A&F University)
Local Conditional Entropy For Amenable Group Actions
For a countable discrete amenable group action, we study two types of measure-theoretical entropies and the concept of topological conditional entropy, both for finite measurable covers conditioned by finite partitions. Using an orbital approach, we establish a local conditional variational principle for an amenable group action. Moreover, we study the concept of conditional entropy tuples. At the end, we introduce the notion of conditional metric mean dimensions and present a corresponding variational principle.
Manuscript.
2024/10/11, 10:00 a.m., Tencent Meeting
Zhang Jiashu (Westlake University)
Homogeneous Besov Spaces in Dunkl Setting
The purpose of this paper is to characterize the homogeneous Besov space in the Dunkl setting. We utilize a new discrete reproducing formula, that is, the building blocks are differences of the Dunkl-Poisson kernel which involves both the Euclidean metric and the Dunkl metric. To introduce the Besov spaces in the Dunkl setting, new test functions and distributions are introduced, and a new decomposition is established.
2024/04/13, 13:00 p.m., Tencent Meeting
Wang Tao (Nankai University)
General relativistic stochastic thermodynamics
Based on the recent work [1,2], we formulate the first law and the second law of stochastic thermodynamics in the framework of general relativity. These laws are established for a charged Brownian particle moving in a heat reservoir and subjecting to an external electromagnetic field in generic stationary spacetime background, and in order to maintain general covariance, they are presented respectively in terms of the divergences of the energy current and the entropy density current. The stability of the equilibrium state is also analyzed.
Article 0, Article 1, Article 2. Two appears in Journal of Statistical Physics.
2024/03/16, 13:00 p.m., Tencent Meeting Password: 789A
Sheng Xi (University of Science and Technology of China)
Stochastic Approximation Algorithms Whose Averages are Competitive
This report discusses a class of stochastic approximation algorithms for iterative processes. Under the assumption of large deviations, the relationship between the long time behavior of the iterative process and the solution flow of the mean field is discussed. When this mean field satisfies a special property, competition, we show that the final behavior of the iterative process asymptotically approximates to some invariant manifold of co-dimension 1. Further, we use a similar approximation algorithm to study the stochastic stability of competing systems and have similar conclusions.
2024/02/23, 10:00 a.m., Tencent Meeting
Wang Haoming (Sun Yat-sen University)
Hierarchy of Maximal ideals in the Banach Algebra II
Based on the series talk I, we discuss applications of results of the C*-algebra to the quantum mechanics.
Manuscript.
2024/02/02, 13:00 p.m., Tencent Meeting
Wang Haoming (Sun Yat-sen University)
Hierarchy of Maximal ideals in the Banach Algebra I
This paper introduces two topologies, namely the weak*-topology (also known as the product topology) and the Zariski topology on the set of maximal ideals in the Banach algebra using both analytical and algebraic methods. It proves that under the condition of separability, the set of maximal ideals endowed with the weak*-topology is second countable and metrizable, and it demonstrates that the two topologies are homeomorphic. We illustrate examples such as the continuous function ring \(C(X)\), where \(X\) is a compact Hausdorff space and the \(l^p\) space for \(1 \leq p < +\infty\).
Manuscript, Slides