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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2013
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| _version_ | 1826264603696300032 |
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| author | Duminil-Copin, H Hammond, A |
| author_facet | Duminil-Copin, H Hammond, A |
| author_sort | Duminil-Copin, H |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T20:10:30Z |
| format | Journal article |
| id | oxford-uuid:2a64c5b4-73d4-438f-a585-0e56d97687b8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:10:30Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:2a64c5b4-73d4-438f-a585-0e56d97687b82022-03-26T12:24:44ZSelf-Avoiding Walk is Sub-BallisticJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2a64c5b4-73d4-438f-a585-0e56d97687b8EnglishSymplectic Elements at Oxford2013Duminil-Copin, HHammond, AWe 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. |
| spellingShingle | Duminil-Copin, H Hammond, A Self-Avoiding Walk is Sub-Ballistic |
| title | Self-Avoiding Walk is Sub-Ballistic |
| title_full | Self-Avoiding Walk is Sub-Ballistic |
| title_fullStr | Self-Avoiding Walk is Sub-Ballistic |
| title_full_unstemmed | Self-Avoiding Walk is Sub-Ballistic |
| title_short | Self-Avoiding Walk is Sub-Ballistic |
| title_sort | self avoiding walk is sub ballistic |
| work_keys_str_mv | AT duminilcopinh selfavoidingwalkissubballistic AT hammonda selfavoidingwalkissubballistic |