Proof of the Conjecture that the Planar Self-Avoiding Walk has Root Mean Square Displacement Exponent 3/4
| dc.creator | Hueter, Irene | |
| dc.date | 2001-08-10 | |
| dc.date | 2001-08-17 | |
| dc.date.accessioned | 2026-07-07T04:42:56Z | |
| dc.date.available | 2026-07-07T04:42:56Z | |
| dc.description | This paper proves the long-standing open conjecture rooted in chemical physics (Flory (1949)) that the self-avoiding walk (SAW) in the square lattice has root mean square displacement exponent ν= 3/4. This value is an instance of the formula ν=1 on Z and ν= max(1/2, 1/4 + 1/d) in Z^d for dimensions d \geq 2, which will be proved in a subsequent paper. This expression differs from the one that Flory's arguments suggested. We consider (a) the point process of self-intersections defined via certain paths of the symmetric simple random walk in Z^2 and (b) a ``weakly self-avoiding cone process'' relative to this point process when in a certain "shape". We derive results on the asymptotic expected distance of the weakly SAW with parameter β>0 from its starting point, from which a number of distance exponents are immediately collectable for the SAW as well. Our method employs the Palm distribution of the point process of self-intersection points in a cone. | |
| dc.description | 32 pages Change to first version: The lower bound for the normalized first two moments of the distance of the weakly SAW from its starting point is not uniform in βas βtends to infinity | |
| dc.identifier | https://arxiv.org/abs/math/0108077 | |
| dc.identifier | http://arxiv.org/abs/math/0108077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62003 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60G50 (Primary) 60D05, 60G57 (Secondary) | |
| dc.title | Proof of the Conjecture that the Planar Self-Avoiding Walk has Root Mean Square Displacement Exponent 3/4 | |
| dc.type | text |