Mathematical Sciences: Percolation and Random Graphs
{'Code': '03040107', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Peter Arzberger', 'PO_EMAI': None, 'PO_PHON': None}
The principal investigator will continue his work in the                   percolation models and random graphs.  The common aspect of both                subjects involves the study of graphs in which each edge is                     present with a probability p.  Such random graphs provide as                    models for percolation depending on the properties of these                     graphs.  Dr. Wierman's major concern is the determination of the                critical probabilities such that a particular property is present               or absent according to whether the probability p exceeds the                    critical probability or not.  The particular properties                         investigated include asymptotic distribution of subgraph counts,                and existence of infinite open clusters.  The major tool used is                that of the duality.  Dr. Wierman has extended the concept of                   duality to many percolation models where the classical duality                  does not apply.  A major motivation for this research is                        applications to phase transitions and critical phenomena.
{'FirstName': 'John', 'LastName': 'Wierman', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John C Wierman', 'EmailAddress': 'wierman@jhu.edu', 'NSF_ID': '000428764', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Johns Hopkins University', 'CityName': 'BALTIMORE', 'ZipCode': '212182608', 'PhoneNumber': '4439971898', 'StreetAddress': '3400 N CHARLES ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Maryland', 'StateCode': 'MD', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'MD07', 'ORG_UEI_NUM': 'FTMTDMBR29C7', 'ORG_LGL_BUS_NAME': 'THE JOHNS HOPKINS UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1263', 'Text': 'PROBABILITY'}
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