Self-avoiding trails and walks and the radius of gyration exponent.
Preprint (2003)

We confirm that the root mean square displacement and the radius of gyration exponents of the self-avoiding trail (SAT) in Z² equal 3/4, as predicted in the mathematical physics literature. Moreover, we prove that the SAT in Z^d for d>2 has lower and upper displacement and radius of gyration exponents in [1/4 + 1/d , 1/2 + 1/2d]. These inequalities are as well shared by the displacement exponent of the self-avoiding walk, as shown in earlier work of Hueter, and its radius of gyration exponent, as argued here. We show that the upper (lower) radius of gyration and displacement exponents of the SAT coincide for every d. We apply the approach introduced in a previous paper and utilize the weakly self-avoiding cone process defined via the spatial process of self-intersection events at bonds or sites of Z^d.