HAUSDORFF DIMENSION OF THE DOUBLE POINT SET OF THE WESTWATER PROCESS

Let X={Xi}t∈[0,1]be the Westwater process which is the coordinate process under3-dimensional polymer measure v（g）constructed by J.Westwater.In this paper,theHausdorff dimension problem for the double point set of X is investigated.As a result,it is proved thatdim D2=1,v（g）-a.e.,where D2={x∈R3:X=X?=x for some s【t∈[0,1]}is the double point set of

Let X = {X(t)}t is-an-element-of [0,1] be the Westwater process which is the coordinate process under 3-dimensional polymer measure nu(g) constructed by J. Westwater. In this paper, the Hausdorff dimension problem for the double point set of X is investigated. As a result, it is proved that dim D2 = 1, nu(g)-a.e., where D2 = {x is-an-element-of R3: X(s) = X(s) = x for some s < t is-an-element-of [0, 1]} is the double point set of X.