LEADER 03878nam 2200649 450 001 9910813659503321 005 20170822144216.0 010 $a1-4704-0410-9 035 $a(CKB)3360000000464993 035 $a(EBL)3114132 035 $a(SSID)ssj0000973374 035 $a(PQKBManifestationID)11514577 035 $a(PQKBTitleCode)TC0000973374 035 $a(PQKBWorkID)10959539 035 $a(PQKB)10793581 035 $a(MiAaPQ)EBC3114132 035 $a(RPAM)13588825 035 $a(PPN)195416961 035 $a(EXLCZ)993360000000464993 100 $a20150417h20042004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMutually catalytic super branching random walks $elarge finite systems and renormalization analysis /$fJ. T. Cox, D. A. Dawson, A. Greven 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2004. 210 4$dİ2004 215 $a1 online resource (97 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 171, Number 809 300 $a"Volume 171, Number 809 (second of 4 numbers)." 311 $a0-8218-3542-4 320 $aIncludes bibliographical references (p. 95-97). 327 $a""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 meana???field finite system scheme""; ""2 Results: Renormalization analysis and corresponding basic limiting dynamics""; ""(a) The multiple spacea???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"" 327 $a""(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 wella???posedness""; ""(c) Properties of the equilibrium T[sup(c,I?³)][sub(I??)]""; ""(d) Stability properties""; ""5 Finite system scheme (Proof of Theorems 1,2)""; ""(a) The finite system scheme (Proof of Theorem 1)"" 327 $a""(b) The meana???field finite system scheme (Proof of Theorem 2)""""6 Multiple spacea???time scale analysis (Proof of Theorem 3, 5)""; ""(a) Hierarchical two level mutually catalytic branching""; ""(b) Hierarchical Ka???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 a??? 8)""; ""(a) Entrance laws of the interaction chain (Proof of Theorem 4)""; ""(b) Clustera???formation (Proof of Theorem 6)""; ""(c) Equilibrium fluctuations (Proof of Theorem 7)"" 327 $a""(d) Meana???field continuum limit (Proof of Proposition 3.1 and Theorem 8)"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 171, Number 809. 606 $aBranching processes 606 $aRandom walks (Mathematics) 606 $aRandom measures 606 $aRenormalization (Physics) 615 0$aBranching processes. 615 0$aRandom walks (Mathematics) 615 0$aRandom measures. 615 0$aRenormalization (Physics) 676 $a519.234 700 $aCox$b J. T.$01606773 702 $aDawson$b Donald A$g(Donald Andrew),$f1937- 702 $aGreven$b Andreas$f1953- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813659503321 996 $aMutually catalytic super branching random walks$93932731 997 $aUNINA