scholarly journals Non-triviality in a totally asymmetric one-dimensional Boolean percolation model on a half-line

2021 ◽  
pp. 109155
Author(s):  
Viktor Bezborodov
Keyword(s):  
Percolation Model ◽  
Half Line ◽  
One Dimensional ◽  
Boolean Percolation

scholarly journals Einstein Relation for Random Walk in a One-Dimensional Percolation Model

2019 ◽  
Vol 176 (4) ◽  
pp. 737-772
Author(s):  
Nina Gantert ◽  
Matthias Meiners ◽  
Sebastian Müller
Keyword(s):  
Random Walk ◽  
Percolation Model ◽  
Einstein Relation ◽  
One Dimensional

Critical behavior of percolation and Markov fields on branching planes

1993 ◽  
Vol 30 (3) ◽  
pp. 538-547 ◽  
Author(s):  
C. Chris Wu
Keyword(s):  
Continuous Function ◽  
Critical Behavior ◽  
Mean Field ◽  
Percolation Model ◽  
Homogeneous Tree ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Percolation Probability ◽  
Triangle Condition ◽  
Markov Fields

For an independent percolation model on, whereis a homogeneous tree andis a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probabilityθ(p) is a continuous function ofpat the critical pointpc, and the critical exponents,γ,δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields onare also obtained.

scholarly journals Correlation length critical exponent as a function of the percolation radius for one-dimensional chains in bond problems

2021 ◽  
Vol 2094 (2) ◽  
pp. 022038
Author(s):  
T V Yakunina ◽  
V N Udodov
Keyword(s):  
Critical Exponent ◽  
Percolation Threshold ◽  
Correlation Length ◽  
Adjacency Matrix ◽  
Nearest Neighbors ◽  
Percolation Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One

Abstract A one-dimensional lattice percolation model is constructed for the problem of constraints flowing along non-nearest neighbors. In this work, we calculated the critical exponent of the correlation length in the one-dimensional bond problem for a percolation radius of up to 6. In the calculations, we used a method without constructing a covering lattice or an adjacency matrix (to find the percolation threshold). The values of the critical exponent of the correlation length were obtained in the one-dimensional bond problem depending on the size of the system and at different percolation radii. Based on original algorithms that operate on a computer faster than standard ones (associated with the construction of a covering lattice), these results are obtained with corresponding errors.

The analytic structure of the reflection coefficient, a sum rule and a complete description of the Weyl m-function of half-line Schrödinger operators with L2-type potentials

2006 ◽  
Vol 136 (3) ◽  
pp. 615-632 ◽  
Author(s):  
Alexei Rybkin
Keyword(s):  
Reflection Coefficient ◽  
Schrödinger Operators ◽  
Half Line ◽  
Analytic Structure ◽  
Schrodinger Operators ◽  
Trace Inequality ◽  
Sum Rule ◽  
One Dimensional ◽  
Upper Half Plane ◽  
Image Position

We prove that the reflection coefficient of one-dimensional Schrödinger operators with potentials supported on a half-line can be represented in the upper half-plane as the quotient of a contractive analytic function and a properly regularized Blaschke product. We apply this fact to obtain a new trace formula and trace inequality for the reflection coefficient that yields a description of the Weyl m-function of Dirichlet half-line Schrödinger operators with slowly decaying potentials q subject to Among others, we also refine the 3/2-Lieb-Thirring inequality.

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