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| '''Thomas C. Spencer''' (born December 24, 1946) is an American [[mathematical physicist]], known in particular for important contributions to [[constructive quantum field theory]], [[statistical mechanics]], and [[spectral theory]] of random operators.<ref name=ias>[http://www.ias.edu/people/faculty-and-emeriti/spencer IAS website]</ref> Since 1986, he is professor of mathematics at the [[Institute for Advanced Study]]. He is a member of the [[United States National Academy of Sciences]],<ref name=ias/> and the recipient of the [[Dannie Heineman Prize for Mathematical Physics]] (joint with [[Jürg Fröhlich]], "''For their joint work in providing rigorous mathematical solutions to some outstanding problems in statistical mechanics and field theory.''").<ref>[http://www.aps.org/programs/honors/prizes/heineman.cfm APS website]</ref><ref>[http://www.aps.org/programs/honors/prizes/prizerecipient.cfm?last_nm=Spencer&first_nm=Thomas&year=1991 1991 Dannie Heineman Prize for Mathematical Physics Recipient], [[American Physical Society]]. Accessed June 24, 2011</ref> | | I'm Mitchell and I live with my husband and our three children in Stord, in the south part. My hobbies are Slot Car Racing, Shortwave listening and Cheerleading.<br><br>My web-site :: [http://adultwebmastermeeting.com/showthread.php?mode=hybrid&t=7178 hd porn] |
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| ==Main Results==
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| * Together with [[James Glimm]] and [[Arthur Jaffe]] he invented the [[cluster expansion]] approach to quantum field theory that is widely used in [[constructive quantum field theory|constructive field theory]].<ref>{{cite journal|first1=J|last1=Glimm|last2=Jaffe|first2=A|last3=Spencer|first3=T|title=The Wightman axioms and particle structure in the <math>P(\phi)_{2}</math> quantum field model|journal=Ann. of Math|year=1974|volume=100|pages=585–632|jstor=1970959}}</ref>
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| * Together with [[Jürg Fröhlich]] and [[Barry Simon]], he invented the approach of the [[infrared bound]], which has now become a classical tool to derive phase transitions in various models of statistical mechanics.<ref>{{cite journal|last1=Fröhlich|first1=J.|last2=Simon|first2=B.|last3=Spencer|first3=T.|title=Infrared bounds, phase transitions and continuous symmetry breaking|journal=Comm. Math. Phys.|volume=50|issue=1|year=1976|pages=79–95|
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| url=http://www.springerlink.com/content/p000130r85020560/}}</ref>
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| * Together with [[Jürg Fröhlich]], he devised a 'multi-scale analysis' to provide, for the first time, mathematical proofs of: the [[Kosterlitz–Thouless transition]],<ref>{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=The Kosterlitz–Thouless transition in two-dimensional abelian spin systems and the Coulomb gas|journal=Comm. Math. Phys.|year=1981|volume=81|issue=4|pages=527–602|url=http://projecteuclid.org/euclid.cmp/1103920388}}</ref> the phase transition in the one-dimensional ferromagnetic Ising model with interactions <math> J_{x,y}\sim |x-y|^{-2} </math><ref>{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=The phase transition in the one-dimensional Ising model with 1/''r''<sup>2</sup> interaction energy.|journal=Comm. Math. Phys.|year=1982|volume=84|issue=1|pages=87–101|url=http://www.springerlink.com/content/wu3782848714tt0l}}</ref> and [[Anderson localization]] in arbitrary [[dimension (vector space)|dimension]].<ref>{{cite journal|last1=Fröhlich|first1=J.|last2=Spencer|first2=T.|title=Absence of diffusion in the Anderson tight binding model for large disorder or low energy.|journal=Comm. Math. Phys.|year=1983|volume=88|issue=2|pages=151–184|url=http://projecteuclid.org/getRecord?id=euclid.cmp/1103922279}}</ref>
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| * Together with [[David Brydges]], he proved that the [[scaling limit]] of the [[self-avoiding walk]] in [[dimension (vector space)|dimension]] greater or equal than 5 is [[normal distribution|Gaussian]], with [[variance]] growing linearly in time.<ref>{{cite journal|last1=Brydges|first1=D.|last2=Spencer|first2=T.|title=Self-avoiding walk in 5 or more dimensions|journal=Comm. Math. Phys.|year=1985|volume=97|issue=1–2|pages=125–148|url=http://projecteuclid.org/euclid.cmp/1103941982}}</ref> To achieve this result, they invented the technique of the [[lace expansion]] that since then has had wide application in probability on graphs.<ref>{{cite book|last1=Slade|first1=G.|title=The lace expansion and its applications |series=Lecture Notes in Mathematics|volume=1879| publisher=Springer|year=2006|url=http://www.springer.com/mathematics/probability/book/978-3-540-31189-8}}</ref>
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| ==References==
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| {{Reflist|2}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Spencer, Thomas
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| | SHORT DESCRIPTION = American mathematical physicist
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| | DATE OF BIRTH = December 24, 1946
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| {{DEFAULTSORT:Spencer, Thomas}}
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| [[Category:1946 births]]
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| [[Category:Living people]]
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| [[Category:Mathematical physicists]]
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| [[Category:Members of the United States National Academy of Sciences]]
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