scholarly journals Exit probability in a one-dimensional nonlinearq-voter model

2011 ◽  
Vol 84 (3) ◽  
Author(s):  
Piotr Przybyła ◽  
Katarzyna Sznajd-Weron ◽  
Maciej Tabiszewski
Keyword(s):  
Voter Model ◽  
One Dimensional ◽  
Exit Probability

scholarly journals Estimates of the Exit Probability for Two Correlated Brownian Motions

2013 ◽  
Vol 45 (01) ◽  
pp. 37-50 ◽  
Author(s):  
Jinghai Shao ◽  
Xiuping Wang
Keyword(s):  
Brownian Motion ◽  
Correlation Coefficient ◽  
Reflection Principle ◽  
Brownian Motions ◽  
One Dimensional ◽  
Exit Probability ◽  
Explicit Formulae

Given two correlated Brownian motions (X t ) t≥ 0 and (Y t ) t≥ 0 with constant correlation coefficient, we give the upper and lower estimations of the probability ℙ(max0 ≤s≤t X s ≥ a, max0 ≤s≤t Y s ≥ b) for any a,b,t > 0 through explicit formulae. Our strategy is to establish a new reflection principle for two correlated Brownian motions, which can be viewed as an extension of the reflection principle for one-dimensional Brownian motion. Moreover, we also consider the nonexit probability for linear boundaries, i.e. ℙ (X t ≤ a t+c,Y t ≤ b t+d, 0≤ t≤T) for any constants a, b≥0 and c,d, T > 0.

scholarly journals Estimates of the Exit Probability for Two Correlated Brownian Motions

2013 ◽  
Vol 45 (1) ◽  
pp. 37-50 ◽  
Author(s):  
Jinghai Shao ◽  
Xiuping Wang
Keyword(s):  
Brownian Motion ◽  
Correlation Coefficient ◽  
Reflection Principle ◽  
Brownian Motions ◽  
One Dimensional ◽  
Exit Probability ◽  
Explicit Formulae

Given two correlated Brownian motions (Xt)t≥ 0 and (Yt)t≥ 0 with constant correlation coefficient, we give the upper and lower estimations of the probability ℙ(max0 ≤s≤tXs≥ a, max0 ≤s≤tYs≥ b) for any a,b,t > 0 through explicit formulae. Our strategy is to establish a new reflection principle for two correlated Brownian motions, which can be viewed as an extension of the reflection principle for one-dimensional Brownian motion. Moreover, we also consider the nonexit probability for linear boundaries, i.e. ℙ (Xt ≤ at+c,Yt ≤ bt+d, 0≤ t≤T) for any constants a, b≥0 and c,d, T > 0.

scholarly journals One-dimensional Voter Model Interface Revisited

2011 ◽  
Vol 16 (0) ◽  
pp. 792-800
Author(s):  
Siva Athreya ◽  
Rongfeng Sun
Keyword(s):  
Voter Model ◽  
One Dimensional

scholarly journals Species exclusion and coexistence in a noisy voter model with a competition-colonization tradeoff

2020 ◽  
Author(s):  
Ricardo Martinez-Garcia ◽  
Cristóbal López ◽  
Federico Vazquez
Keyword(s):  
Lattice Site ◽  
Nearest Neighbor ◽  
External Noise ◽  
Joint Effect ◽  
The Other ◽  
Voter Model ◽  
Stable Phase ◽  
One Dimensional ◽  
Stable Coexistence ◽  
Loop Dynamics

We introduce an asymmetric noisy voter model to study the joint effect of immigration and a competition-dispersal tradeoff in the dynamics of two species competing for space on a one-dimensional lattice. Individuals of one species can invade a nearest-neighbor site in the lattice, while individuals of the other species are able to invade sites at any distance but are less competitive locally, i.e., they establish with a probability g≤ 1. The model also accounts for immigration, modeled as an external noise that may spontaneously replace an individual at a lattice site by another individual of the other species. This combination of mechanisms gives rise to a rich variety of outcomes for species competition, including exclusion of either species, mono-stable coexistence of both species at different population proportions, and bi-stable coexistence with proportions of populations that depend on the initial condition. Remarkably, in the bi-stable phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to an irreversible loop dynamics that may cause the loss of the species with shorter dispersal range.

Transition to Fully or Partially Arrested State in Coupled Logistic Maps on a Ladder

2021 ◽  
Vol 31 (12) ◽  
pp. 2150185
Author(s):  
Nitesh D. Shambharkar ◽  
Ankosh D. Deshmukh ◽  
Prashant M. Gade
Keyword(s):  
Long Range ◽  
Domain Walls ◽  
Voter Model ◽  
Zero Temperature ◽  
Nonlinear Case ◽  
Linear Coupling ◽  
One Dimensional ◽  
Antiferromagnetic Ordering ◽  
Ferromagnetic Ordering ◽  
The Given

Layered structures are an object of interest for theoretical and experimental reasons. In this work, we study coupled map lattice on a ladder. The ladder consists of two one-dimensional chains coupled at every point. We study linearly and nonlinearly coupled logistic maps in this system and study transition to nonzero persistence, in particular. We coarse-grain the variable value by assigning spin [Formula: see text] ([Formula: see text]) to sites that have value greater (less) than the fixed point and compute the number of sites that have not changed their spin values at all even times till the given time [Formula: see text]. The fraction of such sites at a given time [Formula: see text] is known as persistence. In our system, we observe a power-law of persistence at the critical value of coupling. This transition is also accompanied by long-range antiferromagnetic ordering for nonlinear coupling and long-range ferromagnetic ordering for linear coupling. The number of domain walls decay as [Formula: see text] at the critical point in both cases. The persistence exponent is 0.375 for a nonlinear case with two layers which is an exponent for the voter model on the ladder as well as for the Ising model at zero temperature or voter model in 1D. For linear coupling, we obtain a smaller persistence exponent.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Sign in / Sign up

Export Citation Format

Share Document