Approximate upper bounds for the critical probability of oriented percolation in two dimensions based on rapidly mixing Markov chains

1997 ◽  
Vol 34 (04) ◽  
pp. 859-867
Author(s):  
Béla Bollabás ◽  
Alan Stacey
Keyword(s):  
Monte Carlo ◽  
Markov Chains ◽  
Monte Carlo Simulations ◽  
Statistical Tests ◽  
Upper Bounds ◽  
Two Dimensions ◽  
Oriented Percolation ◽  
Critical Probability ◽  
Confidence Levels

We develop a technique for establishing statistical tests with precise confidence levels for upper bounds on the critical probability in oriented percolation. We use it to give pc < 0.647 with a 99.999967% confidence. As Monte Carlo simulations suggest that pc ≈ 0.6445, this bound is fairly tight.

Approximate upper bounds for the critical probability of oriented percolation in two dimensions based on rapidly mixing Markov chains

1997 ◽  
Vol 34 (4) ◽  
pp. 859-867 ◽  
Author(s):  
Béla Bollabás ◽  
Alan Stacey
Keyword(s):  
Monte Carlo ◽  
Markov Chains ◽  
Monte Carlo Simulations ◽  
Statistical Tests ◽  
Upper Bounds ◽  
Two Dimensions ◽  
Oriented Percolation ◽  
Critical Probability ◽  
Confidence Levels

We develop a technique for establishing statistical tests with precise confidence levels for upper bounds on the critical probability in oriented percolation. We use it to givepc< 0.647 with a 99.999967% confidence. As Monte Carlo simulations suggest thatpc≈ 0.6445, this bound is fairly tight.

Upper bounds for the critical probability of oriented percolation in two dimensions

1993 ◽  
Vol 440 (1908) ◽  
pp. 201-220 ◽  
Keyword(s):  
Upper Bound ◽  
Upper Bounds ◽  
Two Dimensions ◽  
Oriented Percolation ◽  
Bond Percolation ◽  
Critical Probability ◽  
Site Percolation

We give a method for obtaining upper bounds on the critical probability in oriented bond percolation in two dimensions. This method enables us to prove that the critical probability is at most 0.6863, greatly improving the best published upper bound, 0.84. We also prove that our method can be used to give arbitrarily good upper bounds. We also use a slight variant of our method to obtain an upper bound of 0.72599 for the critical probability in oriented site percolation.

Transition under noise in the Sznajd model on square lattice

2016 ◽  
Vol 27 (03) ◽  
pp. 1650026 ◽  
Author(s):  
F. W. S. Lima
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Social Behavior ◽  
Monte Carlo Simulations ◽  
Order Phase Transition ◽  
Opinion Dynamics ◽  
Two Dimensions ◽  
Square Lattice ◽  
Behavior Model ◽  
Second Order Phase Transition

In order to describe the formation of a consensus in human opinion dynamics, in this paper, we study the Sznajd model with probabilistic noise in two dimensions. The time evolution of this system is performed via Monte Carlo simulations. This social behavior model with noise presents a well defined second-order phase transition. For small enough noise q < 0.33 most agents end up sharing the same opinion.

Monte Carlo simulations of hard cyclic pentamers in two dimensions

1993 ◽  
Vol 78 (6) ◽  
pp. 1513-1526 ◽  
Author(s):  
A. Brańka ◽  
K.W. Wojciechowski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Two Dimensions

Random-Number Generation

1991 ◽  
Vol 02 (01) ◽  
pp. 296-299
Author(s):  
A. COMPAGNER
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Large Scale ◽  
Random Number ◽  
Statistical Tests ◽  
Random Number Generation ◽  
Operational Definition ◽  
Random Numbers ◽  
The Many ◽  
Definition Of

In large-scale Monte Carlo simulations, reliable random numbers will soon be needed at bit rates of 1 GHz or more. Therefore, existing recipes for the generation of random numbers have to be improved. This is not easy, due to the many unrelated and laborious statistical tests needed to compensate for the lack of an accepted and operational definition of randomness. When however the notion of randomness as a complete absence of all correlations is made precise, a practical approach results.

Dimensional Crossover in the Growth of Depletion Zone in a Rectangular Capillary: Experiments and Monte Carlo Simulations

2003 ◽  
Vol 790 ◽  
Author(s):  
Sung Hyun Park ◽  
Hailin Peng ◽  
Panos Argyrakis ◽  
Haim Taitelbaum ◽  
Raoul Kopelman
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Reaction Zone ◽  
Two Dimensions ◽  
Finite Width ◽  
Dimensional Crossover ◽  
Depletion Zone ◽  
Diffusion Limited ◽  
Boundary Information ◽  
Specific Fraction

ABSTRACTThe diffusion-limited kinetics of the growth of depletion zone around a static point trap in a thin, long stripe geometry was studied using a laser photobleaching experiment of fluorescein dye inside a rectangular capillary. The dynamics of the depletion zone was monitored by the θ-distance, defined as the distance from the trap to the point where the reactant concentration has been depleted to the specific fraction of its initial bulk value. A dimensional crossover from two dimensions to one dimension, due to the finite width of the reaction zone, was observed. The crossover seems to occur for all θ values concurrently when the depletion zone touches the boundary for the first time, suggesting that the boundary information spreads faster than diffusion. Monte Carlo simulations were performed to support the experimental results. The crossover time (τc) is found to scale with the width (L) of the rectangular reaction zone as τc ∼ L2, as expected from the Einstein's diffusion law.

scholarly journals An Inclusive Performance Analysis of Single-branch Single-relay AF Transmission in a Mixed Rayleigh-Nakagami-m Fading Environment

2019 ◽  
Vol 3 ◽  
pp. 39-48
Author(s):  
Slimane Benmahmoud
Keyword(s):  
Monte Carlo ◽  
Performance Analysis ◽  
Monte Carlo Simulations ◽  
Ergodic Capacity ◽  
Upper Bounds ◽  
Amplify And Forward ◽  
Single Relay ◽  
Analytical Expressions ◽  
Af Relaying ◽  
Single Branch

In this paper, the end-to-end performance of a single-branch two-hop amplify-and-forward (AF) relaying network in a mixed Rayleigh-Nakagami-m fading environment, is investigated. Four different fading scenarios and three standard relay configurations for each scenario are considered. Exact analytical expressions for the outage probability and tight upper bounds for the ergodic capacity are derived. Results of Monte Carlo simulations are provided to verify the accuracy of the analytical results.

LONG-RANGE ORDER FOR THE 3-STATE SQUARE LATTICE POTTS MODEL WITH ANTIFERROMAGNETIC “THE MOVE OF THE KNIGHT” INTERACTIONS

1996 ◽  
Vol 10 (15) ◽  
pp. 731-736
Author(s):  
A.V. BAKAEV ◽  
V.I. KABANOVICH
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Potts Model ◽  
Ground State ◽  
Nearest Neighbor ◽  
Two Dimensions ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order

The 3-state square lattice Potts model with interactions of spins belonging to the different sublattices, the nearest-neighbor (NN) interaction and “the move of the knight” (MK) antiferromagnetic interactions which also couples spins on the sublattice A to spins on B, is studied by Monte Carlo simulations. It is shown that the MK-interactions stabilizes the BSS phase in two dimensions, preserving macroscopic degeneracy of the ground state. In a range of competing ferromagnetic (NN) interactions “stripes” or “double-stripes” phases are found.

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