Self-Avoiding Walk is Sub-Ballistic
We prove that self-avoiding walk on ℤd is sub-ballistic in any dimension d ≥ 2. That is,writing {double pipe}u{double pipe} for the Euclidean norm of u ∈ ℤd, and PSAWn for the uniform measure on self-avoiding walks γ: {0,...,n} → ℤd for which γ0 = 0, we show that,for each v > 0, there exists...
| Príomhchruthaitheoirí: | , |
|---|---|
| Formáid: | Journal article |
| Teanga: | English |
| Foilsithe / Cruthaithe: |
2013
|
| Achoimre: | We prove that self-avoiding walk on ℤd is sub-ballistic in any dimension d ≥ 2. That is,writing {double pipe}u{double pipe} for the Euclidean norm of u ∈ ℤd, and PSAWn for the uniform measure on self-avoiding walks γ: {0,...,n} → ℤd for which γ0 = 0, we show that,for each v > 0, there exists ε > 0 such that, for each n ∈ ℕ, PSAWn(max {double pipe}γk{double pipe}: 0 ≤ k ≤ n} ≥ vn) ≤ e-εen. © 2013 Springer-Verlag Berlin Heidelberg. |
|---|