Hitting probabilities of random covering sets in tori and metric spaces

TY - JOUR

T1 - Hitting probabilities of random covering sets in tori and metric spaces

AU - Järvenpää, Esa

AU - Järvenpää, Maarit

AU - Koivusalo, Henna

AU - Li, Bing

AU - Suomala, Ville

AU - Xiao, Yimin

N1 - © 2017, The Author(s).

PY - 2017/1/5

Y1 - 2017/1/5

N2 - We provide sharp lower and upper bounds for the Hausdorff dimension of the intersection of a typical random covering set with a fixed analytic set both in Ahlfors regular metric spaces and in the $d$-dimensional torus. In metric spaces, we consider covering sets generated by balls and, in the torus, we deal with general analytic generating sets.

AB - We provide sharp lower and upper bounds for the Hausdorff dimension of the intersection of a typical random covering set with a fixed analytic set both in Ahlfors regular metric spaces and in the $d$-dimensional torus. In metric spaces, we consider covering sets generated by balls and, in the torus, we deal with general analytic generating sets.

KW - math.PR

KW - math.CA

KW - math.DS

U2 - 10.1214/16-EJP4658

DO - 10.1214/16-EJP4658

M3 - Article

SN - 1083-6489

VL - 22

SP - 1

EP - 18

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - paper no. 1

ER -