Myopic non-intersection in a periodic potential
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918046459756544 |
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| author | Arista, Jonas Remenik, Daniel Sepúlveda, Avelio |
| author_facet | Arista, Jonas Remenik, Daniel Sepúlveda, Avelio |
| contents | We introduce a class of Markov processes conditioned to avoid intersection over a moving time window of length T>0, a setting we refer to as myopic non-intersection. In particular, we study a system of myopic non-intersecting Brownian motions subject to a periodic potential. Our focus lies in understanding the interplay between the confining effect of the potential and the repulsion induced by the non-intersection constraint. We show that, in the long time limit, and as both T and the strength of the potential become large, the model converges to a system of myopic non-intersecting random walks, which transitions between standard non-intersection dynamics and exclusion behavior. The main technical contribution of the paper is the introduction of an algorithm, based on a modification of the acceptance-rejection sampling scheme, that provides an explicit construction of myopically constrained systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05246 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Myopic non-intersection in a periodic potential Arista, Jonas Remenik, Daniel Sepúlveda, Avelio Probability Mathematical Physics We introduce a class of Markov processes conditioned to avoid intersection over a moving time window of length T>0, a setting we refer to as myopic non-intersection. In particular, we study a system of myopic non-intersecting Brownian motions subject to a periodic potential. Our focus lies in understanding the interplay between the confining effect of the potential and the repulsion induced by the non-intersection constraint. We show that, in the long time limit, and as both T and the strength of the potential become large, the model converges to a system of myopic non-intersecting random walks, which transitions between standard non-intersection dynamics and exclusion behavior. The main technical contribution of the paper is the introduction of an algorithm, based on a modification of the acceptance-rejection sampling scheme, that provides an explicit construction of myopically constrained systems. |
| title | Myopic non-intersection in a periodic potential |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2506.05246 |