A RANDOM WALK ON A NON-INTERSECTING TWO-SIDED RANDOM WALK TRACE IS SUBDIFFUSIVE IN LOW DIMENSIONS

作者：Shiraishi Daisuke^*

来源：Transactions of the American Mathematical Society, 2018, 370(7): 4525-4558.

DOI：10.1090/tran/5737

Let ((S) over bar (1),(S) over bar (2)) be the two-sided random walks in Z(d) (d = 2, 3) conditioned so that (S) over bar (1)[0, infinity) boolean AND (S) over bar (2)[1, infinity) = theta, which was constructed by the author in 2012. We prove that the number of global cut times up to n grows like n(3/8) for d = 2. In particular, we show that each (S) over bar (i) has infinitely many global cut times with probability one. Using this property, we prove that the simple random walk on (S) over bar (1)[0, infinity) boolean OR (S) over bar (2) [0, infinity) is subdiffusive for d = 2. We show the same result for d = 3.

• 出版日期2018-7