The right tail exponent of the Tracy–Widom $\beta $ distribution

Laure Dumaz; Bálint Virág

Displaying similar documents to “The right tail exponent of the Tracy–Widom $β$ distribution”

A continuous mapping theorem for the argmin-set functional with applications to convex stochastic processes

Dietmar Ferger (2021)

Kybernetika

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For lower-semicontinuous and convex stochastic processes $Z_{n}$ and nonnegative random variables $ϵ_{n}$ we investigate the pertaining random sets $A (Z_{n}, ϵ_{n})$ of all $ϵ_{n}$ -approximating minimizers of $Z_{n}$ . It is shown that, if the finite dimensional distributions of the $Z_{n}$ converge to some $Z$ and if the $ϵ_{n}$ converge in probability to some constant $c$ , then the $A (Z_{n}, ϵ_{n})$ converge in distribution to $A (Z, c)$ in the hyperspace of Vietoris. As a simple corollary we obtain an extension of several argmin-theorems in the literature. In particular,...

On asymmetric distributions of copula related random variables which includes the skew-normal ones

Ayyub Sheikhi, Fereshteh Arad, Radko Mesiar (2022)

Kybernetika

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Assuming that $C_{X, Y}$ is the copula function of $X$ and $Y$ with marginal distribution functions $F_{X} (x)$ and $F_{Y} (y)$ , in this work we study the selection distribution $Z \overset{d}{=} (X | Y \in T)$ . We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.

On reliability analysis of consecutive $k$ -out-of- $n$ systems with arbitrarily dependent components

Ebrahim Salehi (2016)

Applications of Mathematics

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In this paper, we consider the linear and circular consecutive $k$ -out-of- $n$ systems consisting of arbitrarily dependent components. Under the condition that at least $n - r + 1$ components ( $r \leq n$ ) of the system are working at time $t$ , we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive $k$ -out-of- $n$ systems. In the following, we investigate the inactivity time of the component with lifetime...

Local equivalence of some maximally symmetric $(2, 3, 5)$ -distributions II

Matthew Randall (2025)

Archivum Mathematicum

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We show the change of coordinates that maps the maximally symmetric $(2, 3, 5)$ -distribution given by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation to the flat Cartan distribution. This establishes the local equivalence between the maximally symmetric $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy distribution and the flat Cartan or Hilbert-Cartan distribution. We give the set of vector fields parametrised by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation and the corresponding Ricci-flat conformal scale...

Weakly nonlinear stochastic CGL equations

Sergei B. Kuksin (2013)

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

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We consider the linear Schrödinger equation under periodic boundary conditions, driven by a random force and damped by a quasilinear damping: $\frac{d}{d t} u + i (- Δ + V (x)) u = ν (Δ u - γ_{R} {| u |}^{2 p} u - i γ_{I} {| u |}^{2 q} u) + \sqrt{ν} η (t, x) . (*)$ The force $η$ is white in time and smooth in $x$ ; the potential $V (x)$ is typical. We are concerned with the limiting, as $ν \to 0$ , behaviour of solutions on long time-intervals $0 \leq t \leq ν^{- 1} T$ , and with behaviour of these solutions under the double limit $t \to \infty$ and $ν \to 0$ . We show that these two limiting behaviours may be described in terms of solutions for the( $*$ ) which is a well...

G-tridiagonal majorization on $𝐌_{n, m}$

Ahmad Mohammadhasani, Yamin Sayyari, Mahdi Sabzvari (2021)

Communications in Mathematics

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For $X, Y \in 𝐌_{n, m}$ , it is said that $X$ is majorized by $Y$ (and it is denoted by $X ≺_{g t} Y$ ) if there exists a tridiagonal g-doubly stochastic matrix $A$ such that $X = A Y$ . In this paper, the linear preservers and strong linear preservers of $≺_{g t}$ are characterized on $𝐌_{n, m}$ .

Scale-free percolation

Maria Deijfen, Remco van der Hofstad, Gerard Hooghiemstra (2013)

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

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We formulate and study a model for inhomogeneous long-range percolation on $ℤ^{d}$ . Each vertex $x \in ℤ^{d}$ is assigned a non-negative weight $W_{x}$ , where ${(W_{x})}_{x \in ℤ}^{d}$ are i.i.d. random variables. Conditionally on the weights, and given two parameters $α, λ g t; 0$ , the edges are independent and the probability that there is an edge between $x$ and $y$ is given by $p_{x y} = 1 - exp {- λ W_{x} W_{y} {/ | x - y |}^{α}}$ . The parameter $λ$ is the percolation parameter, while $α$ describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether...

On bilinear forms based on the resolvent of large random matrices

Walid Hachem, Philippe Loubaton, Jamal Najim, Pascal Vallet (2013)

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

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Consider a $N \times n$ non-centered matrix $𝛴_{n}$ with a separable variance profile: $𝛴_{n} = \frac{D_{n}^{1 / 2} X_{n} {\tilde{D}}_{n}^{1 / 2}}{\sqrt{n}} + A_{n} .$ Matrices $D_{n}$ and ${\tilde{D}}_{n}$ are non-negative deterministic diagonal, while matrix $A_{n}$ is deterministic, and $X_{n}$ is a random matrix with complex independent and identically distributed random variables, each with mean zero and variance one. Denote by $Q_{n} (z)$ the resolvent associated to $𝛴_{n} 𝛴_{n}^{*}$ , i.e. $Q_{n} (z) = {(𝛴_{n} 𝛴_{n}^{*} - z I_{N})}^{- 1} .$ Given two sequences of deterministic vectors $(u_{n})$ and $(v_{n})$ with bounded Euclidean norms, we study the limiting behavior of the random bilinear form:...

Initial measures for the stochastic heat equation

Daniel Conus, Mathew Joseph, Davar Khoshnevisan, Shang-Yuan Shiu (2014)

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

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We consider a family of nonlinear stochastic heat equations of the form $\partial_{t} u = ℒ u + σ (u) \dot{W}$ , where $\dot{W}$ denotes space–time white noise, $ℒ$ the generator of a symmetric Lévy process on $𝐑$ , and $σ$ is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure $u_{0}$ . Tight a priori bounds on the moments of the solution are also obtained. In the particular case that $ℒ f = c f^{''}$ for some $c g t; 0$ , we prove that if $u_{0}$ is a finite measure of compact support, then the...

Global approximations for the γ-order Lognormal distribution

Thomas L. Toulias (2013)

Discussiones Mathematicae Probability and Statistics

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A generalized form of the usual Lognormal distribution, denoted with $_{γ}$ , is introduced through the γ-order Normal distribution $_{γ}$ , with its p.d.f. defined into (0,+∞). The study of the c.d.f. of $_{γ}$ is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.

Row Hadamard majorization on $𝐌_{m, n}$

Abbas Askarizadeh, Ali Armandnejad (2021)

Czechoslovak Mathematical Journal

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An $m \times n$ matrix $R$ with nonnegative entries is called row stochastic if the sum of entries on every row of $R$ is 1. Let $𝐌_{m, n}$ be the set of all $m \times n$ real matrices. For $A, B \in 𝐌_{m, n}$ , we say that $A$ is row Hadamard majorized by $B$ (denoted by $A ≺_{R H} B)$ if there exists an $m \times n$ row stochastic matrix $R$ such that $A = R \circ B$ , where $X \circ Y$ is the Hadamard product (entrywise product) of matrices $X, Y \in 𝐌_{m, n}$ . In this paper, we consider the concept of row Hadamard majorization as a relation on $𝐌_{m, n}$ and characterize the structure of all linear operators $T : 𝐌_{m, n} \to 𝐌_{m, n}$ preserving...

On the distribution of $(k, r)$ -integers in Piatetski-Shapiro sequences

Teerapat Srichan (2021)

Czechoslovak Mathematical Journal

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A natural number $n$ is said to be a $(k, r)$ -integer if $n = a^{k} b$ , where $k > r > 1$ and $b$ is not divisible by the $r$ th power of any prime. We study the distribution of such $(k, r)$ -integers in the Piatetski-Shapiro sequence ${⌊ n^{c} ⌋}$ with $c > 1$ . As a corollary, we also obtain similar results for semi- $r$ -free integers.

On the combinatorial structure of $0 / 1$ -matrices representing nonobtuse simplices

Jan Brandts, Abdullah Cihangir (2019)

Applications of Mathematics

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A $0 / 1$ -simplex is the convex hull of $n + 1$ affinely independent vertices of the unit $n$ -cube $I^{n}$ . It is nonobtuse if none of its dihedral angles is obtuse, and acute if additionally none of them is right. Acute $0 / 1$ -simplices in $I^{n}$ can be represented by $0 / 1$ -matrices $P$ of size $n \times n$ whose Gramians $G = P^{⊤} P$ have an inverse that is strictly diagonally dominant, with negative off-diagonal entries. In this paper, we will prove that the positive part $D$ of the transposed inverse $P^{- ⊤}$ of $P$ is doubly stochastic and has the...

On a fixobject property for $l^{c} β$ -semigroupoids

M. Đurić (1973)

Matematički Vesnik

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Perron-Frobenius operators and the Klein-Gordon equation

Francisco Canto-Martín, Håkan Hedenmalm, Alfonso Montes-Rodríguez (2014)

Journal of the European Mathematical Society

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For a smooth curve $Γ$ and a set $Λ$ in the plane $ℝ^{2}$ , let $A C (Γ; Λ)$ be the space of finite Borel measures in the plane supported on $Γ$ , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on $Λ$ . Following [12], we say that $(Γ, Λ)$ is a Heisenberg uniqueness pair if $A C (Γ; Λ) = {0}$ . In the context of a hyperbola $Γ$ , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets $Λ$ of a collection of solutions to the Klein-Gordon equation. In this work, we mainly...

On linear preservers of two-sided gut-majorization on $𝐌_{n, m}$

Asma Ilkhanizadeh Manesh, Ahmad Mohammadhasani (2018)

Czechoslovak Mathematical Journal

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For $X, Y \in 𝐌_{n, m}$ it is said that $X$ is gut-majorized by $Y$ , and we write $X ≺_{gut} Y$ , if there exists an $n$ -by- $n$ upper triangular g-row stochastic matrix $R$ such that $X = R Y$ . Define the relation $\sim_{gut}$ as follows. $X \sim_{gut} Y$ if $X$ is gut-majorized by $Y$ and $Y$ is gut-majorized by $X$ . The (strong) linear preservers of $≺_{gut}$ on $ℝ^{n}$ and strong linear preservers of this relation on $𝐌_{n, m}$ have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of $\sim_{gut}$ on $ℝ^{n}$ and $𝐌_{n, m}$ .

Displaying similar documents to “The right tail exponent of the Tracy–Widom β distribution”

Displaying similar documents to “The right tail exponent of the Tracy–Widom $β$ distribution”