Fluctuation of planar Brownian loop capturing large area
We consider a planar Brownian loop $B$ that is run for a time $T$ and conditioned on the event that its range encloses the unusually high area of $\pi T^2$, with $T$ being large. We study the deviation of the range of the conditioned process $X$ from a circle of radius $T$, as a model for the fluctu...
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1797080218406486016 |
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| author | Hammond, A Peres, Y |
| author_facet | Hammond, A Peres, Y |
| author_sort | Hammond, A |
| collection | OXFORD |
| description | We consider a planar Brownian loop $B$ that is run for a time $T$ and conditioned on the event that its range encloses the unusually high area of $\pi T^2$, with $T$ being large. We study the deviation of the range of the conditioned process $X$ from a circle of radius $T$, as a model for the fluctuation of a phase boundary. This deviation is measured by means of the inradius and outradius of the region enclosed by the range of $X$. We prove that in a typical realization of the conditioned measure, each of these quantities differs from $T$ by at most $T^{2/3 + \epsilon}$. |
| first_indexed | 2024-03-07T00:56:59Z |
| format | Journal article |
| id | oxford-uuid:886b1601-fec3-4c6c-ae90-2c121f25be34 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:56:59Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:886b1601-fec3-4c6c-ae90-2c121f25be342022-03-26T22:17:04ZFluctuation of planar Brownian loop capturing large areaJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:886b1601-fec3-4c6c-ae90-2c121f25be34EnglishSymplectic Elements at Oxford2004Hammond, APeres, YWe consider a planar Brownian loop $B$ that is run for a time $T$ and conditioned on the event that its range encloses the unusually high area of $\pi T^2$, with $T$ being large. We study the deviation of the range of the conditioned process $X$ from a circle of radius $T$, as a model for the fluctuation of a phase boundary. This deviation is measured by means of the inradius and outradius of the region enclosed by the range of $X$. We prove that in a typical realization of the conditioned measure, each of these quantities differs from $T$ by at most $T^{2/3 + \epsilon}$. |
| spellingShingle | Hammond, A Peres, Y Fluctuation of planar Brownian loop capturing large area |
| title | Fluctuation of planar Brownian loop capturing large area |
| title_full | Fluctuation of planar Brownian loop capturing large area |
| title_fullStr | Fluctuation of planar Brownian loop capturing large area |
| title_full_unstemmed | Fluctuation of planar Brownian loop capturing large area |
| title_short | Fluctuation of planar Brownian loop capturing large area |
| title_sort | fluctuation of planar brownian loop capturing large area |
| work_keys_str_mv | AT hammonda fluctuationofplanarbrownianloopcapturinglargearea AT peresy fluctuationofplanarbrownianloopcapturinglargearea |