Moments and Lyapunov exponents for the parabolic Anderson model
We study the parabolic Anderson model in (1+1) dimensions with nearest neighbor jumps and space–time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we...
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| Format: | Article |
| Language: | en_US |
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Institute of Mathematical Statistics
2015
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| Online Access: | http://hdl.handle.net/1721.1/92805 https://orcid.org/0000-0002-2913-5238 |
| _version_ | 1826192323827990528 |
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| author | Borodin, Alexei Corwin, Ivan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Corwin, Ivan |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | We study the parabolic Anderson model in (1+1) dimensions with nearest neighbor jumps and space–time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders. |
| first_indexed | 2024-09-23T09:10:01Z |
| format | Article |
| id | mit-1721.1/92805 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:10:01Z |
| publishDate | 2015 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | mit-1721.1/928052022-09-30T13:51:06Z Moments and Lyapunov exponents for the parabolic Anderson model Borodin, Alexei Corwin, Ivan Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei We study the parabolic Anderson model in (1+1) dimensions with nearest neighbor jumps and space–time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders. National Science Foundation (U.S.) (Grant DMS-10-56390) 2015-01-12T20:26:57Z 2015-01-12T20:26:57Z 2014-06 2013-06 Article http://purl.org/eprint/type/JournalArticle 1050-5164 http://hdl.handle.net/1721.1/92805 Borodin, Alexei, and Ivan Corwin. “Moments and Lyapunov Exponents for the Parabolic Anderson Model.” The Annals of Applied Probability 24, no. 3 (June 2014): 1172–1198. © 2014 Institute of Mathematical Statistics https://orcid.org/0000-0002-2913-5238 en_US http://dx.doi.org/10.1214/13-aap944 Annals of Applied Probability Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Mathematical Statistics Institute of Mathematical Sciences |
| spellingShingle | Borodin, Alexei Corwin, Ivan Moments and Lyapunov exponents for the parabolic Anderson model |
| title | Moments and Lyapunov exponents for the parabolic Anderson model |
| title_full | Moments and Lyapunov exponents for the parabolic Anderson model |
| title_fullStr | Moments and Lyapunov exponents for the parabolic Anderson model |
| title_full_unstemmed | Moments and Lyapunov exponents for the parabolic Anderson model |
| title_short | Moments and Lyapunov exponents for the parabolic Anderson model |
| title_sort | moments and lyapunov exponents for the parabolic anderson model |
| url | http://hdl.handle.net/1721.1/92805 https://orcid.org/0000-0002-2913-5238 |
| work_keys_str_mv | AT borodinalexei momentsandlyapunovexponentsfortheparabolicandersonmodel AT corwinivan momentsandlyapunovexponentsfortheparabolicandersonmodel |