Article Contents
Article Contents

# Ultrametric logarithm laws I

• 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.
Mathematics Subject Classification: 37A17, 37D40, 11K60.

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