Ultrametric logarithm laws I
J. S. Athreya Anish Ghosh Amritanshu Prasad
We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are $S$-arithmetic Diophantine approximation results and logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on trees.
keywords: Diophantine approximation local fields. Shrinking target properties logarithm laws

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