Permutations in competing growth processes and balls-in-bins
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918156659851264 |
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| author | Bäumler, Johannes Iyer, Tejas |
| author_facet | Bäumler, Johannes Iyer, Tejas |
| contents | Consider a model of $N$ independent, increasing $\mathbb{N}_0$-valued processes, with random, independent waiting times between jumps. It is known that there is either an emergent `leader', in which a single process possesses the maximal value for all sufficiently large times, or every pair of processes alternates leadership infinitely often. We show that in the latter regime, almost surely, one sees every possible permutation of rankings of processes infinitely often. In the case that the waiting times are exponentially distributed, this proves a conjecture from Spencer (appearing in a paper from Oliveira) on the `balls-in-bins' process with feedback [Conjecture 1, Combin. Probab. Comput. 17(1):87-110, (2008)]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_07104 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permutations in competing growth processes and balls-in-bins Bäumler, Johannes Iyer, Tejas Probability Combinatorics 60G51, 60J74, 91B70 Consider a model of $N$ independent, increasing $\mathbb{N}_0$-valued processes, with random, independent waiting times between jumps. It is known that there is either an emergent `leader', in which a single process possesses the maximal value for all sufficiently large times, or every pair of processes alternates leadership infinitely often. We show that in the latter regime, almost surely, one sees every possible permutation of rankings of processes infinitely often. In the case that the waiting times are exponentially distributed, this proves a conjecture from Spencer (appearing in a paper from Oliveira) on the `balls-in-bins' process with feedback [Conjecture 1, Combin. Probab. Comput. 17(1):87-110, (2008)]. |
| title | Permutations in competing growth processes and balls-in-bins |
| topic | Probability Combinatorics 60G51, 60J74, 91B70 |
| url | https://arxiv.org/abs/2510.07104 |