Abstract
In the previous decades, the theory of first passage percolation became a highly important area of probability theory. In this work, we will observe what can be said about the corresponding structure if we forget about the probability measure defined on the product space of edges and simply consider topology in the terms of residuality. We focus on interesting questions arising in the probabilistic setup that make sense in this setting, too. We will see that certain classical almost sure events, as the existence of geodesics have residual counterparts, while the notion of the limit shape or time constants gets as chaotic as possible.
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The author was supported by the ÚNKP-17-2 New National Excellence of the Hungarian Ministry of Human Capacities, and by the Hungarian National Research, Development and Innovation Office–NKFIH, Grant 124003.
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Maga, B. Baire categorical aspects of first passage percolation. Acta Math. Hungar. 156, 145–171 (2018). https://doi.org/10.1007/s10474-018-0840-9
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DOI: https://doi.org/10.1007/s10474-018-0840-9