03180nam 2200601 450 991082777380332120170822144316.01-4704-0440-0(CKB)3360000000465023(EBL)3114064(SSID)ssj0000973841(PQKBManifestationID)11533030(PQKBTitleCode)TC0000973841(PQKBWorkID)10984723(PQKB)11682354(MiAaPQ)EBC3114064(RPAM)14038297(PPN)195417275(EXLCZ)99336000000046502320050715h20052005 uy| 0engur|n|---|||||txtccrA random tiling model for two dimensional electrostatics /Mihai CiucuProvidence, Rhode Island :American Mathematical Society,[2005]©20051 online resource (162 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 839"Volume 178, number 839 (third of 5 numbers)."0-8218-3794-X Includes bibliographical references (page 144).""Contents""; ""Abstract""; ""Part A. A Random Tiling Model for Two Dimensional Electrostatics""; ""1. Introduction""; ""2. Definitions, statement of results and physical interpretation""; ""3. Reduction to boundary-influenced correlations""; ""4. A simple product formula for correlations along the boundary""; ""5. A (2m+2n)-fold sum for Ï?[sub(b)]""; ""6. Separation of the (2m+2n)-fold sum for Ï?[sub(b)] in terms of 4mn-fold integrals""; ""7. The asymptotics of the T[sup((n))]'s and T'[sup((n))]'s""; ""8. Replacement of the T[sup((k))]'s and T'[sup((k))]'s by their asymptotics""""9. Proof of Proposition 7.2""""10. The asymptotics of a multidimensional Laplace integral""; ""11. The asymptotics of Ï?[sub(b)]. Proof of Theorem 2.2""; ""12. Another simple product formula for correlations along the boundary""; ""13. The asymptotics of Ï?[sub(b)]. Proof of Theorem 2.1""; ""14. A conjectured general two dimensional Superposition Principle""; ""15. Three dimensions and concluding remarks""; ""Bibliography""; ""Part B. Plane Partitions I: A Generalization of MacMahon's Formula""; ""1. Introduction""; ""2. Two families of regions""""3. Reduction to simply-connected regions""""4. Recurrences for M(R[sub(1,q)](x)) and M(R[sub(1,q)](x))""; ""5. Proof of Proposition 2.1""; ""6. The guessing of M(R[sub(1,q)](x)) and M(R[sub(1,q)](x))""; ""Bibliography""Memoirs of the American Mathematical Society ;no. 839.Tiling (Mathematics)ElectrostaticsStatistical mechanicsTiling (Mathematics)Electrostatics.Statistical mechanics.510 s537/.2Ciucu Mihai1968-1671646MiAaPQMiAaPQMiAaPQBOOK9910827773803321A random tiling model for two dimensional electrostatics4049214UNINA