Effect of symmetry breaking on two-dimensional random walks

1995 ◽  
Vol 52 (4) ◽  
pp. 4516-4519 ◽  
Author(s):  
P. Alpatov ◽  
L. E. Reichl
Keyword(s):  
Symmetry Breaking ◽  
Random Walks ◽  
Two Dimensional

scholarly journals Stability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking

2013 ◽  
Vol 45 (3) ◽  
pp. 1871-1885 ◽  
Author(s):  
C. Bardos ◽  
M. C. Lopes Filho ◽  
Dongjuan Niu ◽  
H. J. Nussenzveig Lopes ◽  
E. S. Titi
Keyword(s):  
Symmetry Breaking ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Viscous Incompressible Flows

scholarly journals Symmetry breaking and gap opening in two-dimensional hexagonal lattices

2011 ◽  
Vol 13 (1) ◽  
pp. 013026 ◽  
Author(s):  
D Malterre ◽  
B Kierren ◽  
Y Fagot-Revurat ◽  
C Didiot ◽  
F J García de Abajo ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Two Dimensional ◽  
Gap Opening

scholarly journals Variance of Voltages in a Lattice Coulomb Gas

2021 ◽  
Vol 186 (1) ◽  
Author(s):  
Diana Conache ◽  
Markus Heydenreich ◽  
Franz Merkl ◽  
Silke W. W. Rolles
Keyword(s):  
High Temperature ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Temperature Regime ◽  
Gaussian Model ◽  
Coulomb Gas ◽  
Two Dimensional ◽  
Discrete Gaussian Model ◽  
Dimensional Lattice ◽  
The Difference

AbstractWe study the behavior of the variance of the difference of energies for putting an additional electric unit charge at two different locations in the two-dimensional lattice Coulomb gas in the high-temperature regime. For this, we exploit the duality between this model and a discrete Gaussian model. Our estimates follow from a spontaneous symmetry breaking in the latter model.

scholarly journals Limit theorems for isotropic random walks on triangle buildings

2002 ◽  
Vol 73 (3) ◽  
pp. 301-334 ◽  
Author(s):  
Marc Lindlbauer ◽  
Michael Voit
Keyword(s):  
Limit Theorem ◽  
Random Walks ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Two Dimensional ◽  
Littlewood Polynomials ◽  
Large Numbers ◽  
Moment Functions ◽  
Vertex Sets ◽  
Isotropic Random

AbstractThe spherical functions of triangle buildings can be described in terms of certain two-dimensional orthogonal polynomials on Steiner's hypocycloid which are closely related to Hall-Littlewood polynomials. They lead to a one-parameter family of two-dimensional polynimial hypergroups. In this paper we investigate isotropic random walks on the vertex sets of triangle buildings in terms of their projections to these hypergroups. We present strong laws of large numbers, a central limit theorem, and a local limit theorem; all these results are well-known for homogeneous trees. Proofs are based on moment functions on hypergroups and on explicit expansions of the hypergroup characters in terms of certain two-dimensional Tchebychev polynimials.

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