Asymptotic behavior of a tagged particle in simple exclusion processes

2000 ◽  
Vol 31 (3) ◽  
pp. 241-275 ◽  
Author(s):  
C. Landim ◽  
S. Olla ◽  
S. R. S. Varadhan
Keyword(s):  
Asymptotic Behavior ◽  
Exclusion Processes ◽  
Tagged Particle ◽  
Simple Exclusion

scholarly journals Limit theorems for the tagged particle in exclusion processes on regular trees

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Dayue Chen ◽  
Peng Chen ◽  
Nina Gantert ◽  
Dominik Schmid
Keyword(s):  
Limit Theorems ◽  
Exclusion Processes ◽  
Tagged Particle

Physical mechanisms in impacts of interaction factors on totally asymmetric simple exclusion processes

2019 ◽  
Vol 33 (20) ◽  
pp. 1950217 ◽  
Author(s):  
Yu-Qing Wang ◽  
Jia-Wei Wang ◽  
Bing-Hong Wang
Keyword(s):  
Stochastic Dynamics ◽  
Exclusion Process ◽  
Characteristic Parameter ◽  
Exclusion Processes ◽  
Physical Mechanisms ◽  
Interaction Factor ◽  
Interaction Factors ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The Impact

Exclusion processes are hot study issues in statistical physics and corresponding complex systems. Among fruitful exclusion processes, totally asymmetric simple exclusion process (namely, TASEP) attracts much attention due to its insight physical mechanisms in understanding such nonequilibrium dynamical processes. However, interactions among isolated TASEP are the core of controlling the dynamics of multiple TASEPs that are composed of a certain amount of isolated one-dimensional TASEP. Different from previous researches, the interaction factor is focused on the critical characteristic parameter used to depict the interaction intensity of these components of TASEPs. In this paper, a much weaker constraint condition [Formula: see text] is derived as the analytical expression of interaction factor. Self-propelled particles in the subsystem [Formula: see text] of multiple TASEPs can perform hopping forward at [Formula: see text], moving into the target site of the (i − 1)th TASEP channel at [Formula: see text] or updating into the (i + 1)th TASEP channel at [Formula: see text]. The comparison of this proposed interaction factor and other previous factors is performed by investigating the computational efficiency of obtaining analytical solutions and simulation ones of order parameters of the proposed TASEP system. Obtained exact solutions are observed to match well with Monte Carlo simulations. This research attempts to have a more comprehensive interpretation of physical mechanisms in the impact of interaction factors on TASEPs, especially corresponding to stochastic dynamics of self-propelled particles in such complex statistical dynamical systems.

First displacement time of a tagged particle in a stochastic cluster in a simple exclusion process with random slow bonds

2019 ◽  
Vol 51 (03) ◽  
pp. 717-744
Author(s):  
Adriana Uquillas ◽  
Adilson Simonis
Keyword(s):  
Poisson Process ◽  
Exclusion Process ◽  
Upper And Lower Bounds ◽  
Density Profiles ◽  
Tagged Particle ◽  
Simple Exclusion Process ◽  
Discrete Torus ◽  
Simple Exclusion ◽  
The One ◽  
Initial Measure

AbstractWe consider the nearest-neighbour simple exclusion process on the one-dimensional discrete torus $\mathbb{T}_N=\mathbb{Z}/N\mathbb{Z}$ , with random rates $c_N=\{c_{x,N}\colon x \in \mathbb{T}_N\}$ defined in terms of a homogeneous Poisson process on $\mathbb{R}$ with intensity $\lambda$ . Given a realization of the Poisson process, the jump rate along the edge $\{x,x+1\}$ is 1 if there is not any Poisson mark in $ (x,x+1) $ ; otherwise, it is $\lambda/N,\, \lambda \in( 0,1]$ . The density profile of this process with initial measure associated to an initial profile $\rho_0\colon \mathbb{R} \rightarrow [0,1]$ , evolves as the solution of a bounded diffusion random equation. This result follows from an appropriate quenched hydrodynamic limit. If $\lambda=1$ then $\rho$ is discontinuous at each Poisson mark with passage through the slow bonds, otherwise the conductance at the slow bonds decreases meaning no passage through the slow bonds in the continuum. The main results are concerned with upper and lower quenched and annealed bounds of $T_j$ , where $T_j$ is the first displacement time of a tagged particle in a stochastic cluster of size j (the cluster is defined via specific macroscopic density profiles). It is possible to observe that when time t grows, then $\mathbb{P}\{T_j \geq t\}$ decays quadratically in both the upper and lower bounds, and falls as slow as the presence of more Poisson marks neighbouring the tagged particle, as expected.

scholarly journals EXCLUSION PROCESSES AND BOUNDARY CONDITIONS

2004 ◽  
Vol 18 (01) ◽  
pp. 1-9 ◽  
Author(s):  
FARINAZ ROSHANI ◽  
MOHAMMAD KHORRAMI
Keyword(s):  
Boundary Conditions ◽  
Exclusion Process ◽  
Conditional Probabilities ◽  
Exclusion Processes ◽  
Simple Exclusion Process ◽  
The Family ◽  
Simple Exclusion ◽  
The One ◽  
Push Model ◽  
The Continuum

A family of boundary conditions corresponding to exclusion processes is introduced. This family is a generalization of the boundary conditions corresponding to the simple exclusion process, the drop-push model, and the one-parameter solvable family of pushing processes with certain rates on the continuum.1–3 The conditional probabilities are calculated using the Bethe ansatz, and it is shown that at large times they behave like the corresponding conditional probabilities of the family of diffusion-pushing processes introduced in Refs. 1–3.

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