Related papers: Microlocal analysis of generalized pullbacks of Co…
This paper establishes the equivalence of the Aubin property and the strong regularity for generalized equations over $C^2$-cone reducible sets. This result resolves a long-standing question in variational analysis and extends the…
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…
We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat…
We argue that one can model deviations from the ensemble average in non-equilibrium statistical mechanics by promoting the Boltzmann equation to an equation in terms of {\em functionals} , representing possible candidates for phase space…
We show how the tangent functor extends from ordinary smooth maps to "microformal morphisms" (also called "thick morphisms") of supermanifolds. Microformal morphisms generalize ordinary maps and correspond to formal canonical relations…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
We study some constructions on distributions in a uniform $p$-adic context, and also in large positive characteristic, using model theoretic methods. We introduce a class of distributions which we call distributions of ${\mathscr…
We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasianalytic Gelfand-Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence…
We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the…
In this paper, we present the asymptotic theory for integrated functions of increments of Brownian local times in space. Specifically, we determine their first-order limit, along with the asymptotic distribution of the fluctuations. Our key…
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…
Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of ($\infty$-)categories of spans (or correspondences). In this paper we study the…
In 2014, Voronov introduced the notion of thick morphisms of (super)manifolds as a tool for constructing $L_{\infty}$-morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary smooth maps, but are not maps themselves.…
We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving…
Let $G$ be a compact subgroup of $GL_n(\R)$ acting linearly on a finite dimensional vector space $E$. B. Malgrange has shown that the space $\mathcal{C}^\infty(\R^n,E)^G$ of $\mathcal{C}^\infty$ and $G$-covariant functions is a finite…
We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…
We prove that for Gaussian random normal matrices the correlation function has universal behavior. Using the technique of orthogonal polynomials and identities similar to the Christoffel-Darboux formula, we find that in the limit, as the…
Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…
We define a type of generalized asymptotic series called $v$-asymptotic. We show that every function with moderate growth at infinity has a $v$-asymptotic expansion. We also describe the set of $v$-asymptotic series, where a given function…
The finite subgroups of ${\rm PGL}_2(\mathbb{C})$ are shown to be the only finite groups $G$ with this property: for some integer $r_0$ (depending on $G$), all Galois covers $X\rightarrow \mathbb{P}^1_{\mathbb{C}}$ of group $G$ can be…