Related papers: Grothendieck's Double Limit Theorem and Model Theo…
This thesis discusses the Newtonian limit of General Relativity for static isolated systems with compactly supported matter. We call these systems "geometrostatic" to underline their geometric nature. We introduce new quasi-local notions of…
In this expository article, we summarize what is known about maximum likelihood thresholds of Gaussian models, paying special attention to connections with rigidity theory.
The thermodynamic limit of the Lipkin model is investigated. While the limit turns out to be rather elusive, the analysis gives strong indications that the limit yields two analytically dissociated operators, one for the normal and one for…
We discuss some classical and recent results and open problems on the statistical behavior of ergodic sums above toral translations, and their applications to Diophantine approximations and to ergodic properties of systems related to…
To reveal how nonequilibrium physics and relativity theory intertwine, this articles studies relativistic Brownian motion under cosmic expansion. Two fluctuation theorems for the entropy ds, which is locally produced in this extreme…
In two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a d- dimensional rotationally symmetric stable process. These results allow one to discuss some…
In this paper, we study a two-dimensional Lorentzian problem on the anti-de Sitter plane. Using methods of geometric control theory and differential geometry, it was possible to construct an orthonormal frame, calculate extremal…
We refine results of Gannon [G21, Theorem 4.7] and Simon [S15a, Lemma 2.8] on equivalences of convergent Morley sequences. We then introduce the notion of eventual $NIP$, as a property of a model, and give a variant of [KP18, Corollary…
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we…
This paper is dedicated to the study of the stability of multiplicities of group representations.
The paper extends the well-known Lyusternik-Graves theorem for set-valued mappings to the Holder framework, offers an affirmative answer to an open problem proposed by Dontchev and improves recent results of He and Ng. Primal and dual…
We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination…
In this paper, we study stability and instability problem for type-II partitioning problem. First, we make a complete classification of stable type-II stationary hypersurfaces in a ball in a space form as totally geodesic $n$-balls. Second,…
In this article, we discuss stability of the one-dimensional overdamped Lange\-vin equation in double-well potential. We determine unstable and stable equilibria, and discuss the rate of convergence to stable ones. Also, we derive…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
The past twenty years have seen a resurgence of interest in nonequilibrium thermodynamics, thanks to advances in the theory of stochastic processes and in their thermodynamic interpretation. Fluctuation theorems provide fundamental…
This is a written version of the invited lecture at the 9th European Congress of Mathematics in July 2024 in Sevilla. We review certain new symmetries of Grothendieck rings that have emerged in representation theory.
In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
We revisit the work of To\"en--Vezzosi and Lurie on Grothendieck topologies, using the new tools of acyclic classes and congruences. We introduce a notion of extended Grothendieck topology on any $\infty$-topos, and prove that the poset of…