Exclusion vs Noncolliding Dynamics in Markov Processes
Abstract
Let (ξt)t ≥ 0 be a continuous-time Markov process taking values in a countable state space E. We consider k copies of ξ started from distinct positions, and write X = (Xt)t ≥ 0 for the resulting process of configurations in Ek. We compare two forms of interaction between the particles: the first is conditioning the particles to never collide (noncolliding dynamics), and the second is simply switching off any jumps that would cause two particles to occupy the same position (exclusion dynamics). We show under mild conditions on the tail probabilities of the collision time that the dynamics are related by an explicit exponential martingale change of measure of one another. This generalises a recent result in the integrable probability literature relating TASEP on the ring to asymmetric walkers conditioned to never collide.
Related
- Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions
- Dynamics for exclusion processes with random environments of particle jump rates
- Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: Quantum symmetric simple exclusion and inclusion processes
- Non-equilibrium fluctuations of gradient exclusion processes in dimension d≤ 3
- Hydrodynamic limits of finite range exclusion processes
BibTeX
@misc{shiatis2026exclusion,
title = {{Exclusion vs Noncolliding Dynamics in Markov Processes}},
author = {Rohan Shiatis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00741},
eprint = {2610.00741},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00741},
}
RIS
TY - UNPB
TI - Exclusion vs Noncolliding Dynamics in Markov Processes
AU - Rohan Shiatis
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00741
UR - https://arxiv.org/abs/2610.00741
AB - Let (ξ_t)_t ≥ 0 be a continuous-time Markov process taking values in a countable state space E. We consider k copies of ξ started from distinct positions, and write X = (X_t)_t ≥ 0 for the resulting process of configurations in E^k. We compare two forms of interaction between the particles: the first is conditioning the particles to never collide (noncolliding dynamics), and the second is simply switching off any jumps that would cause two particles to occupy the same position (exclusion dynamics). We show under mild conditions on the tail probabilities of the collision time that the dynamics are related by an explicit exponential martingale change of measure of one another. This generalises a recent result in the integrable probability literature relating TASEP on the ring to asymmetric walkers conditioned to never collide.
ER -