scholarly journals Non-probabilistic fermionic limit shapes

2021 ◽  
Vol 2021 (1) ◽  
pp. 013204
Author(s):  
Saverio Bocini ◽  
Jean-Marie Stéphan
Keyword(s):  
Limit Shapes

scholarly journals Limit Shapes for Gibbs Ensembles of Partitions

2018 ◽  
Vol 172 (6) ◽  
pp. 1545-1563
Author(s):  
Ibrahim Fatkullin ◽  
Valeriy Slastikov
Keyword(s):  
Limit Shapes

scholarly journals Grove Arctic Curves from Periodic Cluster Modular Transformations

2020 ◽  
Author(s):  
Terrence George
Keyword(s):  
Generating Functions ◽  
Gibbs Measures ◽  
The Arctic ◽  
Probability Measures ◽  
Finite Region ◽  
Resistor Network ◽  
Modular Transformations ◽  
Spanning Forests ◽  
Limit Shapes

Abstract Groves are spanning forests of a finite region of the triangular lattice that are in bijection with Laurent monomials that arise in solutions of the cube recurrence. We introduce a large class of probability measures on groves for which we can compute exact generating functions for edge probabilities. Using the machinery of asymptotics of multivariate generating functions, this lets us explicitly compute arctic curves, generalizing the arctic circle theorem of Petersen and Speyer. Our class of probability measures is sufficiently general that the limit shapes exhibit all solid and gaseous phases expected from the classification of ergodic Gibbs measures in the resistor network model.

scholarly journals Integer partitions and exclusion statistics: limit shapes and the largest parts of Young diagrams

2007 ◽  
Vol 2007 (10) ◽  
pp. P10001-P10001 ◽  
Author(s):  
Alain Comtet ◽  
Satya N Majumdar ◽  
Stéphane Ouvry ◽  
Sanjib Sabhapandit
Keyword(s):  
Integer Partitions ◽  
Young Diagrams ◽  
Limit Shapes

scholarly journals Limit Shapes via Bijections

2018 ◽  
Vol 28 (2) ◽  
pp. 187-240 ◽  
Author(s):  
STEPHEN DeSALVO ◽  
IGOR PAK
Keyword(s):  
Scaling Functions ◽  
Integer Partitions ◽  
Limit Shape ◽  
Limit Shapes

We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes continuously in the plane. We start with bijections outlined in [43], and extend them to include limit shapes with different scaling functions.

The limit shapes of midpoint polygons in ℝ3

2019 ◽  
Vol 28 (10) ◽  
pp. 1950062
Author(s):  
Chao Wang ◽  
Zhongzi Wang
Keyword(s):  
Euclidean Space ◽  
Affine Transformation ◽  
Interesting Case ◽  
Dimensional Euclidean Space ◽  
Discrete Version ◽  
Regular Polygons ◽  
Limit Shapes ◽  
Polygonal Knots

For a polygon in the [Formula: see text]-dimensional Euclidean space, we give two kinds of normalizations of its [Formula: see text]th midpoint polygon by a homothetic transformation and an affine transformation, respectively. As [Formula: see text] goes to infinity, the normalizations will approach “regular” polygons inscribed in an ellipse and a generalized Lissajous curve, respectively, where the curves may be degenerate. The most interesting case is when [Formula: see text], where polygons with all its [Formula: see text]th midpoint polygons knotted are discovered and discussed. Such polygonal knots can be seen as a discrete version of the Lissajous knots.

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