03878nam 2200649 450 991081365950332120170822144216.01-4704-0410-9(CKB)3360000000464993(EBL)3114132(SSID)ssj0000973374(PQKBManifestationID)11514577(PQKBTitleCode)TC0000973374(PQKBWorkID)10959539(PQKB)10793581(MiAaPQ)EBC3114132(RPAM)13588825(PPN)195416961(EXLCZ)99336000000046499320150417h20042004 uy 0engur|n|---|||||txtccrMutually catalytic super branching random walks large finite systems and renormalization analysis /J. T. Cox, D. A. Dawson, A. GrevenProvidence, Rhode Island :American Mathematical Society,2004.©20041 online resource (97 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 171, Number 809"Volume 171, Number 809 (second of 4 numbers)."0-8218-3542-4 Includes bibliographical references (p. 95-97).""Contents""; ""0 Introduction""; ""(a) Background and motivation""; ""(b) The model and review of the basic ergodic theory""; ""1 Results: Longtime behavior of large finite systems""; ""(a) The finite system scheme""; ""(b) The meanâ€?field finite system scheme""; ""2 Results: Renormalization analysis and corresponding basic limiting dynamics""; ""(a) The multiple spaceâ€?time scale analysis""; ""(b) The entrance law of the interaction chain""; ""(c) Renormalization analysis and spatial continuum limit""; ""3 Results: Application of renormalization to large scale behavior""""(a) Details on the formation of monotype clusters""""(b) Finer properties of equilibria in the case of coexistence""; ""(c) Finer properties of the continuum limit""; ""(d) Outlook: The problem of universality""; ""4 Preparation: Key technical tools""; ""(a) Duality relations""; ""(b) State space of the process and wellâ€?posedness""; ""(c) Properties of the equilibrium T[sup(c,γ)][sub(Î?)]""; ""(d) Stability properties""; ""5 Finite system scheme (Proof of Theorems 1,2)""; ""(a) The finite system scheme (Proof of Theorem 1)""""(b) The meanâ€?field finite system scheme (Proof of Theorem 2)""""6 Multiple spaceâ€?time scale analysis (Proof of Theorem 3, 5)""; ""(a) Hierarchical two level mutually catalytic branching""; ""(b) Hierarchical Kâ€?level mutually catalytic branching""; ""(c) Conclusion of the Proof of Theorem 3""; ""(d) Proof of Theorem 5""; ""7 Analysis of the interaction chain (Proof Theorem 4, 6 â€? 8)""; ""(a) Entrance laws of the interaction chain (Proof of Theorem 4)""; ""(b) Clusterâ€?formation (Proof of Theorem 6)""; ""(c) Equilibrium fluctuations (Proof of Theorem 7)""""(d) Meanâ€?field continuum limit (Proof of Proposition 3.1 and Theorem 8)""Memoirs of the American Mathematical Society ;Volume 171, Number 809.Branching processesRandom walks (Mathematics)Random measuresRenormalization (Physics)Branching processes.Random walks (Mathematics)Random measures.Renormalization (Physics)519.234Cox J. T.1606773Dawson Donald A(Donald Andrew),1937-Greven Andreas1953-MiAaPQMiAaPQMiAaPQBOOK9910813659503321Mutually catalytic super branching random walks3932731UNINA