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Capacities and Hitting Times for Simple and (critical) Branching Random Walk Sausages

  • Joelle Ishak
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Abstract

For a finite set A⊆ℤd, we study the capacities of a sausage obtained by transporting A along the Minkowski sum of simple or critical branching random walks. We first establish quantitative capacity estimates for the random walk sausage and the branching sausage. This in turn, gives us estimates for the probability that Minkowski sums of a mixture of walks hit a finite set in high dimensions. Our approach is based on an annular decomposition of a critical branching random walk into successive waves, which may have further applications.

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Cite

BibTeXRIS
BibTeX
@misc{ishak2026capacities,
  title = {{Capacities and Hitting Times for Simple and (critical) Branching Random Walk Sausages}},
  author = {Joelle Ishak},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12160},
  eprint = {2610.12160},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12160},
}
RIS
TY  - UNPB
TI  - Capacities and Hitting Times for Simple and (critical) Branching Random Walk Sausages
AU  - Joelle Ishak
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12160
UR  - https://arxiv.org/abs/2610.12160
AB  - For a finite set A⊆ℤ^d, we study the capacities of a sausage obtained by transporting A along the Minkowski sum of simple or critical branching random walks. We first establish quantitative capacity estimates for the random walk sausage and the branching sausage. This in turn, gives us estimates for the probability that Minkowski sums of a mixture of walks hit a finite set in high dimensions. Our approach is based on an annular decomposition of a critical branching random walk into successive waves, which may have further applications.
ER  -