scholarly journals Gibbs measures on permutations over one-dimensional discrete point sets

2015 ◽  
Vol 25 (2) ◽  
pp. 898-929 ◽  
Author(s):  
Marek Biskup ◽  
Thomas Richthammer
Keyword(s):  
Gibbs Measures ◽  
Discrete Point ◽  
Point Sets ◽  
One Dimensional

scholarly journals Matching with shift for one-dimensional Gibbs measures

2009 ◽  
Vol 19 (4) ◽  
pp. 1581-1602
Author(s):  
P. Collet ◽  
C. Giardina ◽  
F. Redig
Keyword(s):  
Gibbs Measures ◽  
One Dimensional

Asymptotics for Minimal Discrete Riesz Energy on Curves in ℝd

2004 ◽  
Vol 56 (3) ◽  
pp. 529-552 ◽  
Author(s):  
A. Martínez-Finkelshtein ◽  
V. Maymeskul ◽  
E. A. Rakhmanov ◽  
E. B. Saff
Keyword(s):  
Jordan Curve ◽  
Hausdorff Measure ◽  
Compact Sets ◽  
Minimizing Sequences ◽  
Point Sets ◽  
Dimensional Hausdorff Measure ◽  
One Dimensional ◽  
Riesz Kernel ◽  
Riesz Energy ◽  
Image Position

AbstractWe consider the s-energy for point sets 𝒵 = {𝒵k,n: k = 0, …, n} on certain compact sets Γ in ℝd having finite one-dimensional Hausdorff measure,is the Riesz kernel. Asymptotics for the minimum s-energy and the distribution of minimizing sequences of points is studied. In particular, we prove that, for s ≥ 1, the minimizing nodes for a rectifiable Jordan curve Γ distribute asymptotically uniformly with respect to arclength as n → ∞.

scholarly journals A Note on Fixed Point Sets and Wedges

1980 ◽  
Vol 23 (4) ◽  
pp. 453-455 ◽  
Author(s):  
John R. Martin ◽  
Sam B. Nadler
Keyword(s):  
Fixed Point ◽  
Closed Subset ◽  
Invariance Property ◽  
Point Sets ◽  
Fixed Point Set ◽  
Nonempty Closed Subset ◽  
One Dimensional ◽  
Point Set ◽  
Fixed Point Sets

A space Z is said to have the complete invariance property (CIP) provided that every nonempty closed subset of Z is the fixed point set of some continuous self-mapping of Z. In this paper it is shown that there exists a one-dimensional contractible planar continuum having CIP whose wedge with itself at a specified point is contractible, planar, and does not have CIP.

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