相关论文: Revisiting jointly firmly nonexpansive families of…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
We study the approximation of conformal mappings with the polynomials defined by Keldysh and Lavrentiev from an extremal problem considered by Julia. These polynomials converge uniformly on the closure of any Smirnov domain to the conformal…
Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…
Uniform asymptotic expansions involving exponential and Airy functions are obtained for Laguerre polynomials $L_{n}^{(\alpha)}(x)$, as well as complementary confluent hypergeometric functions. The expansions are valid for $n$ large and…
We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…
Building on the dictionary between Kleinian groups and rational maps, we establish new connections between the theories of hyperbolic groups and certain iterated maps, regarded as dynamical systems. In order to make the exposition…
In previous work, a class of noninvertible topological dynamical systems $f: X \to X$ was introduced and studied; we called these {\em topologically coarse expanding conformal} systems. To such a system is naturally associated a preferred…
This paper introduces iterated monodromy groups for transcendental functions and discusses them in the simplest setting, for post-singularly finite exponential functions. These groups are self-similar groups in a natural way, based on an…
We leverage the connections between nonexpansive maps, monotone Lipschitz operators, and proximal mappings to obtain near-optimal (i.e., optimal up to poly-log factors in terms of iteration complexity) and parameter-free methods for solving…
The aim of this paper is to give a new description of the geometry appearing in the multi-specialization along a general family of submanifolds of a real analytic manifold (including some important cases as clean intersection or a…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
We present a natural extension of the notion of nondegenerate rational maps (quadrirational maps) to arbitrary dimensions. We refer to these maps as $2^n-$rational maps. In this note we construct a rich family of $2^n-$rational maps. These…
In this paper we generalize standard results about non-commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups. We show in particular that quotient singularities for reductive groups always have…
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better…
We study the large-$N$ behavior of random matrix tuples $Y^N = (Y_1^N,\dots,Y_d^N)$ with joint density proportional to $e^{-N^2 V}$ for some convex function $V$ in non-commuting variables satisfying certain bounds on its second derivative.…
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…
We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms and involve abstract gradient and divergence terms. Our main interest is to provide graph and…
A family of non-conjugate chaotic maps generalizing the well-known logistic function is defined, and some of its basic properties studied. A simple formula for the Lyapunov exponents of all the maps contained in this family is given based…
We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing…
This paper proposes a data-driven approach for constructing firmly nonexpansive operators. We demonstrate its applicability in Plug-and-Play (PnP) methods, where classical algorithms such as Forward-Backward splitting, Chambolle-Pock…