scholarly journals Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process

2020 ◽  
Author(s):  
Eunghyun Lee ◽  
Keyword(s):  
Transition Probabilities ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Initial State ◽  
Exclusion Processes ◽  
Final State ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

We find the formulas of the transition probabilities of the N-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities are written as a determinant when the order of particles in the final state is the same as the order of particles in the initial state.

scholarly journals Combinatorics of the 2-Species Exclusion Processes, Marked Laguerre Histories, and Partially Signed Permutations

10.37236/8910 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Sylvie Corteel ◽  
Arthur Nunge
Keyword(s):  
Exclusion Process ◽  
Point Of View ◽  
Asymmetric Simple Exclusion Process ◽  
Exclusion Processes ◽  
Signed Permutations ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

Starting from the two-species partially asymmetric simple exclusion process, we study a subclass of signed permutations, the partially signed permutations, using the combinatorics of Laguerre histories. From this physical and bijective point of view, we obtain a natural descent statistic on partially signed permutations; as well as partially signed permutations patterns.

scholarly journals Integrability of the Multi-Species TASEP with Species-Dependent Rates

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1578
Author(s):  
Eunghyun Lee
Keyword(s):  
Bethe Ansatz ◽  
Transition Probabilities ◽  
Exclusion Process ◽  
Particle Systems ◽  
Asymmetric Simple Exclusion Process ◽  
Ansatz Method ◽  
Jump Rate ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

Assume that each species l has its own jump rate bl in the multi-species totally asymmetric simple exclusion process. We show that this model is integrable in the sense that the Bethe ansatz method is applicable to obtain the transition probabilities for all possible N-particle systems with up to N different species.

Stochastic comparisons of density profiles for the road-hog process

1991 ◽  
Vol 28 (04) ◽  
pp. 852-863
Author(s):  
Rengarajan Srinivasan
Keyword(s):  
Exclusion Process ◽  
Stochastic Ordering ◽  
Asymmetric Simple Exclusion Process ◽  
The Other ◽  
Density Profiles ◽  
Poisson Input ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The Right

We consider the asymmetric simple exclusion process which starts from a product measure such that all the sites to the left of zero (including zero) are occupied and the right of 0 (excluding 0) are empty. We label the particle initially at 0 as the leading particle. We study the long-term behaviour of this process near large sites when the leading particle's holding time is different from that of the other particles. In particular, we assume that the leading particle moves at a slower rate than the other particles. We call this modified asymmetric simple exclusion process the road-hog process. Coupling and stochastic ordering techniques are used to derive the density profile of this process. Road-hog processes are useful in modelling series of exponential queues with Poisson and non-Poisson input process. The density profiles dramatically illustrate the flow of customers through the queues.

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