Mathematical Sciences: Random Fields
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
The main researcher for this project will be a post-doc to                 the principal investigator.  The researcher will continue his                   work on the random fields.  Infinite dimensional probability                    spaces provide excellent models in the study of Eucleadian                      quantum field theory and equilibrium statistical mechanics.  The                probability spaces providing the models have parameters that                    correspond to temperature, momentum cutoff and coupling constants               etc..  Various phenomena such as phase transition, symmetry                     breaking and consequences of renormalization can be predicted by                varying these perameters.  Except in very simple situations, the                proofs of these predictions are difficult to accomplish                         rigorously.  The researcher will try to attack some of these                    intriguing problems via the use of techniques from nonhomogeneous               Gaussian processes associated with the free Markov field.
{'FirstName': 'Thomas', 'LastName': 'Liggett', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Thomas M Liggett', 'EmailAddress': 'tml@math.ucla.edu', 'NSF_ID': '000478462', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Los Angeles', 'CityName': 'LOS ANGELES', 'ZipCode': '900244200', 'PhoneNumber': '3107940102', 'StreetAddress': '10889 WILSHIRE BLVD STE 700', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '36', 'CONGRESS_DISTRICT_ORG': 'CA36', 'ORG_UEI_NUM': 'RN64EPNH8JC6', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA, LOS ANGELES', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1263', 'Text': 'PROBABILITY'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8702558.xml'}