A stochastic telegraph equation from the six-vertex model
© Institute of Mathematical Statistics, 2019. A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second-order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are proportional to the twodimensional white noise, and solutio...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Institute of Mathematical Statistics
2021
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| Online Access: | https://hdl.handle.net/1721.1/133366 |
| _version_ | 1826197100255248384 |
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| author | Borodin, Alexei Gorin, Vadim |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Gorin, Vadim |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | © Institute of Mathematical Statistics, 2019. A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second-order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are proportional to the twodimensional white noise, and solutions to our equation are two-dimensional random Gaussian fields. We show that such fields arise naturally as asymptotic fluctuations of the height function in a certain limit regime of the stochastic six-vertex model in a quadrant. The corresponding law of large numbers-the limit shape of the height function-is described by the (deterministic) homogeneous telegraph equation. |
| first_indexed | 2024-09-23T10:42:48Z |
| format | Article |
| id | mit-1721.1/133366 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:42:48Z |
| publishDate | 2021 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/1333662024-01-02T15:31:47Z A stochastic telegraph equation from the six-vertex model Borodin, Alexei Gorin, Vadim Massachusetts Institute of Technology. Department of Mathematics © Institute of Mathematical Statistics, 2019. A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second-order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are proportional to the twodimensional white noise, and solutions to our equation are two-dimensional random Gaussian fields. We show that such fields arise naturally as asymptotic fluctuations of the height function in a certain limit regime of the stochastic six-vertex model in a quadrant. The corresponding law of large numbers-the limit shape of the height function-is described by the (deterministic) homogeneous telegraph equation. 2021-10-27T19:52:23Z 2021-10-27T19:52:23Z 2019 2021-05-17T18:25:56Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/133366 en 10.1214/19-AOP1356 The Annals of Probability Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Mathematical Statistics arXiv |
| spellingShingle | Borodin, Alexei Gorin, Vadim A stochastic telegraph equation from the six-vertex model |
| title | A stochastic telegraph equation from the six-vertex model |
| title_full | A stochastic telegraph equation from the six-vertex model |
| title_fullStr | A stochastic telegraph equation from the six-vertex model |
| title_full_unstemmed | A stochastic telegraph equation from the six-vertex model |
| title_short | A stochastic telegraph equation from the six-vertex model |
| title_sort | stochastic telegraph equation from the six vertex model |
| url | https://hdl.handle.net/1721.1/133366 |
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