TY - JOUR
T1 - A tale of two balloons
AU - Angel, Omer
AU - Ray, Gourab
AU - Spinka, Yinon
N1 - Publisher Copyright:
© 2023, Crown.
PY - 2023/4
Y1 - 2023/4
N2 - From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the hyperbolic plane and regular trees. The result for the Euclidean space relies on a novel 0–1 law for stationary processes. Towards establishing the results for the hyperbolic plane and regular trees, we prove an upper bound on the density of any well-separated set in a regular tree which is a factor of an i.i.d. process.
AB - From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the hyperbolic plane and regular trees. The result for the Euclidean space relies on a novel 0–1 law for stationary processes. Towards establishing the results for the hyperbolic plane and regular trees, we prove an upper bound on the density of any well-separated set in a regular tree which is a factor of an i.i.d. process.
UR - http://www.scopus.com/inward/record.url?scp=85148589506&partnerID=8YFLogxK
U2 - 10.1007/s00440-022-01165-6
DO - 10.1007/s00440-022-01165-6
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AN - SCOPUS:85148589506
SN - 0178-8051
VL - 185
SP - 815
EP - 837
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 3-4
ER -