相关论文: Self-Similar Random Processes and Infinite-Dimensi…

The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…

We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular interest, and it is studied in more detail. The main…

We define the manifold of configurations to be the quotient set of $k$ points in Euclidean space identified under congruence, and prove that compact subsets of $\mathbb{R}^d, d \geq 2$, of large Hausdorff dimension have a non-null set of…

We study quantum corrections to hypersurfaces of dimension $d+1>2$ embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and…

We study continuity and discontinuity properties of some popular measure-dimension mappings under some topologies on the space of probability measures in this work. We give examples to show that no continuity can be guaranteed under general…

In this paper we study a homological version of the higher-dimensional divergence invariants defined by Brady and Farb. We show that they are quasi-isometry invariants in the class of proper cocompact Hadamard spaces in the sense of…

Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of…

We make some general remarks on long-ranged configurations in gauge or diffeomorphism invariant theories where the fields are allowed to assume some non vanishing values at spatial infinity. In this case the Gauss constraint only eliminates…

The quantization problem for random fractals presents unique challenges due to the lack of uniform geometric scaling inherent in deterministic systems. In this article, we establish the almost sure quantization dimension for a class of…

In a series of papers Tsirelson constructed from measure types of random sets and generalised random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying…

In this note, we show that determinantal point processes on the real line corresponding to de Branges spaces of entire functions are rigid in the sense of Ghosh-Peres and, under certain additional assumptions, quasi-invariant under the…

In this work the problem about an existence of non-measurable automorphisms of Lie groups finite and as well infinite dimensional over the field of real numbers and also over the non-archimedean local fields is investigated.…

We extend finding geometrically-significant preserved quantities by solving specific PDEs to the affine transformations and subgroups. This can be viewed not only as a purely geometrical problem but also as a subcase of finding physical…

We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topological measures and topological measures on locally compact…

The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…

We explore the structure of the space of quasisymmetric configurations identifying them by their magnetic axes, described as 3D closed curves. We demonstrate that this topological perspective divides the space of all configurations into…

The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…

Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of…

We prove that in dimensions not equal to 4, 5, or 7, the homology and homotopy groups of the classifying space of the topological group of diffeomorphisms of a disk fixing the boundary are finitely generated in each degree. The proof uses…

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…