Proof of the conjecture that the planar self-avoiding walk has distance exponent 3/4.
Preprint (2002)

This paper proves the long-standing open conjecture rooted in chemical physics (P.J. Flory, 1949) that the self-avoiding walk (SAW) in the square lattice has root mean square displacement exponent 3/4. Our approach is to consider a ``weakly self-avoiding cone process" with parameter ß >0, a walk that suppresses self-intersections in a particular cone containing the endpoint of the walk, and to condition on an event which in the limit as ß tends to infinity forces the walk to be self-avoiding.