Generalized Christoffel functions for Jacobi-exponential weights

2013 ◽  
Vol 140 (1-2) ◽  
pp. 71-89 ◽  
Author(s):  
Ying Guang Shi
Keyword(s):  
Exponential Weights ◽  
Christoffel Functions

scholarly journals Orthogonal polynomials for exponential weights x2α(1 – x2)2ρe–2Q(x) on [0, 1)

2020 ◽  
Vol 18 (1) ◽  
pp. 138-149
Author(s):  
Rong Liu
Keyword(s):  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Lagrange Interpolation ◽  
Restricted Range ◽  
Exponential Weights ◽  
Christoffel Functions

Abstract Let Wα,ρ = xα(1 – x2)ρe–Q(x), where α > – $\begin{array}{} \displaystyle \frac12 \end{array}$ and Q is continuous and increasing on [0, 1), with limit ∞ at 1. This paper deals with orthogonal polynomials for the weights $\begin{array}{} \displaystyle W^2_{\alpha, \rho} \end{array}$ and gives bounds on orthogonal polynomials, zeros, Christoffel functions and Markov inequalities. In addition, estimates of fundamental polynomials of Lagrange interpolation at the zeros of the orthogonal polynomial and restricted range inequalities are obtained.

scholarly journals Non-existence of bi-infinite geodesics in the exponential corner growth model

2020 ◽  
Vol 8 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Coarse Graining ◽  
Exponential Weights ◽  
Percolation Process ◽  
Last Passage Percolation ◽  
Corner Growth Model ◽  
And Control

Abstract This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

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