Formula for the Mean Square Displacement Exponent of the Self-Avoiding Walk in 3, 4 and All Dimensions
نویسنده
چکیده
This paper proves the formula
منابع مشابه
A ug 2 00 1 Proof of the Conjecture that the Planar Self - Avoiding Walk has Root Mean Square Displacement Exponent 3 / 4
This paper proves the long-standing open conjecture rooted in chemical physics (Flory (1949) [3]) 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 for dimensions d ≥ 2, which will be proved in a subsequent paper. This expression differs from the one that ...
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This paper proves the long-standing open conjecture rooted in chemical physics (Flory (1949) [3]) that the self-avoiding walk (SAW) in the square lattice has root mean square displacement exponent 3/4. We consider (a) the point process of selfintersections defined via certain paths of the symmetric simple random walk in Z and (b) a “weakly self-avoiding cone process” relative to this point proc...
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