Auer, Peter - In: Statistics & Probability Letters 9 (1990) 5, pp. 403-407
Let S0, S1,..., be a simple symmetric random walk of 2, S0=0, and [xi](x,n)=#{k:0<k[less-than-or-equals, slant]n, Sk=x} be the local time of the random walk. We prove that , where is the circle of radius r and R(n)=exp{(log n)1/2/(log log n)1/2+[var epsilon]}, [var epsilon]>0.