Random walks in 2 dimensions are recurrent whereas in higher dimensions random walks are not. And there is a wonderful colloquialism to remember this. “A drunk [person] will find [their] way home but a drunk bird may get lost forever.”

Random walks in 2 dimensions are recurrent whereas in higher dimensions random walks are not. And there is a wonderful colloquialism by Shizuo Kakutani to remember this: “A drunk man will find his way home but a drunk bird may get lost forever.”

Random walks in 2 dimensions are recurrent whereas in higher dimensions random walks are not. And there is a wonderful colloquialism to remember this. “A drunk man will find his way home but a drunk bird may get lost forever.”

Random walks in 2 dimensions are recurrent whereas in higher dimensions random walks are not. And there is a wonderful colloquialism to remember this. “A drunk [person] will find [their] way home but a drunk bird may get lost forever.”