scholarly journals The critical probability for Voronoi percolation in the hyperbolic plane tends to 1/2

2021 ◽  
Author(s):  
Benjamin T. Hansen ◽  
Tobias Müller
Keyword(s):  
Hyperbolic Plane ◽  
Critical Probability

scholarly journals Upper bounds on the rate of low density stabilizer codes for the quantum erasure channel

2013 ◽  
Vol 13 (9&10) ◽  
pp. 793-826
Author(s):  
Nicolas Delfosse ◽  
Gilles Zemor
Keyword(s):  
Upper Bound ◽  
Percolation Theory ◽  
Hyperbolic Plane ◽  
Upper Bounds ◽  
Low Density ◽  
Critical Probability ◽  
Stabilizer Codes ◽  
Erasure Channel ◽  
Finite Quotients ◽  
Quantum Erasure

Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, $R \leq 1-2p$, for stabilizer codes: we also derive an improved upper bound of the form $R \leq 1-2p-D(p)$ with a function $D(p)$ that stays positive for $0<p<1/2$ and for any family of stabilizer codes whose generators have weights bounded from above by a constant -- low density stabilizer codes. We obtain an application to percolation theory for a family of self-dual tilings of the hyperbolic plane. We associate a family of low density stabilizer codes with appropriate finite quotients of these tilings. We then relate the probability of percolation to the probability of a decoding error for these codes on the quantum erasure channel. The application of our upper bound on achievable rates of low density stabilizer codes gives rise to an upper bound on the critical probability for these tilings.

In a Class With Klein: Generating A Model of the Hyperbolic Plane

PRIMUS ◽  
2012 ◽  
Vol 22 (2) ◽  
pp. 85-96
Author(s):  
Samuel Otten ◽  
Christopher Zin
Keyword(s):  
Hyperbolic Plane

On the inversion of the geodesic Radon transform on the hyperbolic plane

1997 ◽  
Vol 13 (4) ◽  
pp. 1053-1062 ◽  
Author(s):  
Sergei Lissianoi ◽  
Igor Ponomarev
Keyword(s):  
Radon Transform ◽  
Hyperbolic Plane

scholarly journals Fourier transforms of Lipschitz functions on the hyperbolic planeH2

1998 ◽  
Vol 21 (2) ◽  
pp. 397-401 ◽  
Author(s):  
M. S. Younis
Keyword(s):  
Hyperbolic Plane ◽  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Order Of Magnitude ◽  
Complex Valued ◽  
Lipschitz Conditions

The purpose of the present work is to study the order of magnitude of the Fourier transformsfˆ(λ)for largeλof complex-valued functionsf(z)sating certain Lipschitz conditions in the non-Euclidean hyperbolic planeH2.

scholarly journals Simple equation of state for hard disks on the hyperbolic plane

2008 ◽  
Vol 129 (11) ◽  
pp. 116101 ◽  
Author(s):  
Mariano López de Haro ◽  
Andrés Santos ◽  
Santos B. Yuste
Keyword(s):  
Equation Of State ◽  
Hyperbolic Plane ◽  
Simple Equation ◽  
Hard Disks
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