Spatially Independent Martingales Intersections And Applications
DOWNLOAD
Download Spatially Independent Martingales Intersections And Applications PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Spatially Independent Martingales Intersections And Applications book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Spatially Independent Martingales Intersections And Applications
DOWNLOAD
Author : Pablo Shmerkin
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-22
Spatially Independent Martingales Intersections And Applications written by Pablo Shmerkin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-22 with Mathematics categories.
The authors define a class of random measures, spatially independent martingales, which we view as a natural generalization of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian cut-outs. The authors pair the random measures with deterministic families of parametrized measures , and show that under some natural checkable conditions, a.s. the mass of the intersections is Hölder continuous as a function of . This continuity phenomenon turns out to underpin a large amount of geometric information about these measures, allowing us to unify and substantially generalize a large number of existing results on the geometry of random Cantor sets and measures, as well as obtaining many new ones. Among other things, for large classes of random fractals they establish (a) very strong versions of the Marstrand-Mattila projection and slicing results, as well as dimension conservation, (b) slicing results with respect to algebraic curves and self-similar sets, (c) smoothness of convolutions of measures, including self-convolutions, and nonempty interior for sumsets, and (d) rapid Fourier decay. Among other applications, the authors obtain an answer to a question of I. Łaba in connection to the restriction problem for fractal measures.
Elliptic Pdes On Compact Ricci Limit Spaces And Applications
DOWNLOAD
Author : Shouhei Honda
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Elliptic Pdes On Compact Ricci Limit Spaces And Applications written by Shouhei Honda and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.
Cluster Algebras And Triangulated Surfaces Part Ii Lambda Lengths
DOWNLOAD
Author : Sergey Fomin
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
Cluster Algebras And Triangulated Surfaces Part Ii Lambda Lengths written by Sergey Fomin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmüller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface.
Bellman Function For Extremal Problems In Bmo Ii Evolution
DOWNLOAD
Author : Paata Ivanisvili
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
Bellman Function For Extremal Problems In Bmo Ii Evolution written by Paata Ivanisvili and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.
On The Geometric Side Of The Arthur Trace Formula For The Symplectic Group Of Rank 2
DOWNLOAD
Author : Werner Hoffmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
On The Geometric Side Of The Arthur Trace Formula For The Symplectic Group Of Rank 2 written by Werner Hoffmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
The authors study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank over any algebraic number field. In particular, they express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke -functions, and the Shintani zeta function for the space of binary quadratic forms.
Strichartz Estimates And The Cauchy Problem For The Gravity Water Waves Equations
DOWNLOAD
Author : T. Alazard
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-08
Strichartz Estimates And The Cauchy Problem For The Gravity Water Waves Equations written by T. Alazard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Mathematics categories.
This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.
On Mesoscopic Equilibrium For Linear Statistics In Dyson S Brownian Motion
DOWNLOAD
Author : Maurice Duits
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
On Mesoscopic Equilibrium For Linear Statistics In Dyson S Brownian Motion written by Maurice Duits and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with β=2 . Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.
Fourier Analysis And Hausdorff Dimension
DOWNLOAD
Author : Pertti Mattila
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-22
Fourier Analysis And Hausdorff Dimension written by Pertti Mattila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-22 with Mathematics categories.
Modern text examining the interplay between measure theory and Fourier analysis.
Recent Developments In Fractals And Related Fields
DOWNLOAD
Author : Julien Barral
language : en
Publisher: Springer Nature
Release Date : 2025-04-18
Recent Developments In Fractals And Related Fields written by Julien Barral and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-18 with Mathematics categories.
This volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals. It includes both original research contributions, as well as surveys from many of the leading experts on modern fractal geometry theory and applications. The contributions contained in the book stem from the conference “Fractals and Related Fields IV", that was held in 2022 on the Island of Porquerolles, France. Various aspects of fractal geometry in connection with harmonic analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, functional analysis, additive combinatorics, embedding theory, and signal and image processing are addressed within its pages. We hope that the book will be interesting for pure and applied mathematicians in these areas, as well as for other researchers curious to discover more about fractals.
On Non Generic Finite Subgroups Of Exceptional Algebraic Groups
DOWNLOAD
Author : Alastair J. Litterick
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
On Non Generic Finite Subgroups Of Exceptional Algebraic Groups written by Alastair J. Litterick and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.
The study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.