Download or read book The Mother Body Phase Transition in the Normal Matrix Model written by Pavel M. Bleher and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this present paper, the authors consider the normal matrix model with cubic plus linear potential.

Download or read book Progress on the Study of the Ginibre Ensembles written by Sung-Soo Byun and published by Springer Nature. This book was released on with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Traffic Distributions and Independence Permutation Invariant Random Matrices and the Three Notions of Independence written by Camille Male and published by American Mathematical Society. This book was released on 2021-02-10 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. The author first establishes this construction for random matrices and then defines the traffic distribution of random matrices, which is richer than the $^*$-distribution of free probability. The knowledge of the individual traffic distributions of independent permutation invariant families of matrices is sufficient to compute the limiting distribution of the join family. Under a factorization assumption, the author calls traffic independence the asymptotic rule that plays the role of independence with respect to traffic distributions. Wigner matrices, Haar unitary matrices and uniform permutation matrices converge in traffic distributions, a fact which yields new results on the limiting $^*$-distributions of several matrices the author can construct from them. Then the author defines the abstract traffic spaces as non commutative probability spaces with more structure. She proves that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence. A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.

Download or read book Hyponormal Quantization of Planar Domains written by Björn Gustafsson and published by Springer. This book was released on 2017-09-29 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.

Download or read book Gromov Witten Theory of Quotients of Fermat Calabi Yau Varieties written by Hiroshi Iritani and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.

Download or read book Differential Function Spectra the Differential Becker Gottlieb Transfer and Applications to Differential Algebraic K Theory written by Ulrich Bunke and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.

Download or read book Resolvent Heat Kernel and Torsion under Degeneration to Fibered Cusps written by Pierre Albin and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.

Download or read book Local Well Posedness and Break Down Criterion of the Incompressible Euler Equations with Free Boundary written by Chao Wang and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2 +ε. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.

Download or read book Paley Wiener Theorems for a p Adic Spherical Variety written by Patrick Delorme and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C pXq be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley–Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers — rings of multipliers for SpXq and C pXq.WhenX “ a reductive group, our theorem for C pXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step — enough to recover the structure of the Bern-stein center — towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01].

Download or read book Bounded Littlewood Identities written by Eric M. Rains and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a method, based on the theory of Macdonald–Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald’s partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon’s famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers–Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko–Macdonald-type basic hypergeometric series.

Download or read book Linear Dynamical Systems on Hilbert Spaces Typical Properties and Explicit Examples written by S. Grivaux and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigen-values and admits no non-trivial invariant measure, but is densely distri-butionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form “diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift” is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but not ergodic in the Gaussian sense. (iii) There exist Hilbert space operators which are chaotic and U-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not U-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties.

Download or read book Weakly Modular Graphs and Nonpositive Curvature written by Jérémie Chalopin and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article investigates structural, geometrical, and topological characteri-zations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various “nonpositive cur-vature” and “local-to-global” properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a far-reaching common generalization of median graphs (and more generally, of mod-ular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under different disguises (1–skeletons, collinearity graphs, covering graphs, domains, etc.) in several seemingly-unrelated fields of mathematics: * Metric graph theory * Geometric group theory * Incidence geometries and buildings * Theoretical computer science and combinatorial optimization We give a local-to-global characterization of weakly modular graphs and their sub-classes in terms of simple connectedness of associated triangle-square complexes and specific local combinatorial conditions. In particular, we revisit characterizations of dual polar graphs by Cameron and by Brouwer-Cohen. We also show that (disk-)Helly graphs are precisely the clique-Helly graphs with simply connected clique complexes. With l1–embeddable weakly modular and sweakly modular graphs we associate high-dimensional cell complexes, having several strong topological and geometrical properties (contractibility and the CAT(0) property). Their cells have a specific structure: they are basis polyhedra of even 􀀁–matroids in the first case and orthoscheme complexes of gated dual polar subgraphs in the second case. We resolve some open problems concerning subclasses of weakly modular graphs: we prove a Brady-McCammond conjecture about CAT(0) metric on the orthoscheme.

Download or read book The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners written by Paul Godin and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study 2D compressible Euler flows in bounded impermeable domains whose boundary is smooth except for corners. We assume that the angles of the corners are small enough. Then we obtain local (in time) existence of solutions which keep the L2 Sobolev regularity of their Cauchy data, provided the external forces are sufficiently regular and suitable compatibility conditions are satisfied. Such a result is well known when there is no corner. Our proof relies on the study of associated linear problems. We also show that our results are rather sharp: we construct counterexamples in which the smallness condition on the angles is not fulfilled and which display a loss of L2 Sobolev regularity with respect to the Cauchy data and the external forces.

Download or read book Theory of Fundamental Bessel Functions of High Rank written by Zhi Qi and published by American Mathematical Society. This book was released on 2021-02-10 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.

Download or read book Operator Theory on One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus and Spectral Operators written by Jonathan Gantner and published by American Mathematical Society. This book was released on 2021-02-10 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.

Download or read book ojasiewicz Simon Gradient Inequalities for Coupled Yang Mills Energy Functionals written by Paul M Feehan and published by American Mathematical Society. This book was released on 2021-02-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.

Download or read book Hecke Operators and Systems of Eigenvalues on Siegel Cusp Forms written by Kazuyuki Hatada and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.