New stability results for spheres and Wulff shapes

Julien Roth

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Displaying similar documents to “New stability results for spheres and Wulff shapes”

The category of compactifications and its coreflections

Anthony W. Hager, Brian Wynne (2022)

Commentationes Mathematicae Universitatis Carolinae

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We define “the category of compactifications”, which is denoted , and consider its family of coreflections, denoted . We show that is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone $β$ . A $c \in$ implies the assignment to each locally compact, noncompact $Y$ a compactification minimum for membership in the “object-range” of $c$ . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate...

An integral transform and its application in the propagation of Lorentz-Gaussian beams

A. Belafhal, E.M. El Halba, T. Usman (2021)

Communications in Mathematics

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The aim of the present note is to derive an integral transform $I = \int_{0}^{\infty} x^{s + 1} e^{- β x^{2} + γ x} M_{k, ν} (2 ζ x^{2}) J_{μ} (χ x) d x,$ involving the product of the Whittaker function $M_{k, ν}$ and the Bessel function of the first kind $J_{μ}$ of order $μ$ . As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters $k$ and $ν$ of the Whittaker function. Eventually, we show the application of the integral in the propagation of hollow higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system...

Local percolative properties of the vacant set of random interlacements with small intensity

Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov (2014)

Annales de l'I.H.P. Probabilités et statistiques

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Random interlacements at level $u$ is a one parameter family of connected random subsets of $ℤ^{d}$ , $d \geq 3$ ( (2010) 2039–2087). Its complement, the vacant set at level $u$ , exhibits a non-trivial percolation phase transition in $u$ ( (2009) 831–858; (2010) 2039–2087), and the infinite connected component, when it exists, is almost surely unique ( (2009) 454–466). In this paper we study local percolative properties of the vacant set of random...

An explicit integral polynomial whose splitting field has Galois group $W (E_{8})$

Florent Jouve, Emmanuel Kowalski, David Zywina (2008)

Journal de Théorie des Nombres de Bordeaux

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Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group $G$ over $Q$ typically have splitting field with Galois group isomorphic to the Weyl group of $G$ , we construct an explicit monic integral polynomial of degree $240$ whose splitting field has Galois group the Weyl group of the exceptional group of type $E_{8}$ .

Almost sure limit theorems for dependent random variables

Michał Seweryn (2010)

Banach Center Publications

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For a sequence of dependent random variables ${(X_{k})}_{k \in ℕ}$ we consider a large class of summability methods defined by R. Jajte in [] as follows: For a pair of real-valued nonnegative functions g,h: ℝ⁺ → ℝ⁺ we define a sequence of “weighted averages” $1 / g (n) \sum_{k = 1}^{n} (X_{k}) / h (k)$ , where g and h satisfy some mild conditions. We investigate the almost sure behavior of such transformations. We also take a close look at the connection between the method of summation (that is the pair of functions (g,h)) and the coefficients that...

Convergence rates for the full gaussian rough paths

Peter Friz, Sebastian Riedel (2014)

Annales de l'I.H.P. Probabilités et statistiques

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Under the key assumption of finite $ρ$ -variation, $ρ \in [1, 2)$ , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), $ρ = 1$ resp. $ρ = 1 / (2 H)$ , we recover and extend the respective results of ( (2009) 2689–2718) and ( (2012) 518–550). In particular, we establish an a.s. rate $k^{- (1 / ρ - 1 / 2 - ε)}$ , any $ε g t; 0$ , for Wong–Zakai and Milstein-type approximations...

Convolution-dominated integral operators

Gero Fendler, Karlheinz Gröchenig, Michael Leinert (2010)

Banach Center Publications

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For a locally compact group G we consider the algebra CD(G) of convolution-dominated operators on L²(G), where an operator A: L²(G) → L²(G) is called convolution-dominated if there exists a ∈ L¹(G) such that for all f ∈ L²(G) |Af(x)| ≤ a⋆|f|(x), for almost all x ∈ G. (1) The case of discrete groups was treated in previous publications [, ]. For non-discrete groups we investigate a subalgebra of regular convolution-dominated operators generated by product convolution operators, where...

Actions of the additive group $G_{a}$ on certain noncommutative deformations of the plane

Ivan Kaygorodov, Samuel A. Lopes, Farukh Mashurov (2021)

Communications in Mathematics

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We connect the theorems of Rentschler [] and Dixmier [] on locally nilpotent derivations and automorphisms of the polynomial ring $A_{0}$ and of the Weyl algebra $A_{1}$ , both over a field of characteristic zero, by establishing the same type of results for the family of algebras $A_{h} = 〈 x, y ∣ y x - x y = h (x) 〉,$ where $h$ is an arbitrary polynomial in $x$ . In the second part of the paper we consider a field $𝔽$ of prime characteristic and study $𝔽 [t]$ comodule algebra structures on $A_{h}$ . We also compute the Makar-Limanov invariant of absolute...

Ergodic behaviour of “signed voter models”

G. Maillard, T. S. Mountford (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We answer some questions raised by Gantert, Löwe and Steif ( (2005) 767–780) concerning “signed” voter models on locally finite graphs. These are voter model like processes with the difference that the edges are considered to be either positive or negative. If an edge between a site $x$ and a site $y$ is negative (respectively positive) the site $y$ will contribute towards the flip rate of $x$ if and only if the two current spin values are equal (respectively opposed). ...