Mutually catalytic super branching random walks : large finite systems and renormalization analysis / J. T. Cox, D. A. Dawson, A. Greven.

Format:

Book

Author/Creator:

Cox, J. T., author.

Dawson, Donald A. (Donald Andrew), 1937- author.

Greven, Andreas, 1953- author.

Series:

Memoirs of the American Mathematical Society ; Volume 171, Number 809.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 171, Number 809

Language:

English

Subjects (All):

Branching processes.

Random walks (Mathematics).

Random measures.

Renormalization (Physics).

Physical Description:

1 online resource (97 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2004.

Language Note:

English

Summary:

Studies the evolution of the large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. This title introduces the concept of a continuum limit in the hierarchical mean field limit.

Contents:

""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 mean�field finite system scheme""; ""2 Results: Renormalization analysis and corresponding basic limiting dynamics""; ""(a) The multiple space�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 mean�field finite system scheme (Proof of Theorem 2)""""6 Multiple space�time scale analysis (Proof of Theorem 3, 5)""; ""(a) Hierarchical two level mutually catalytic branching""; ""(b) Hierarchical K�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 � 8)""; ""(a) Entrance laws of the interaction chain (Proof of Theorem 4)""; ""(b) Cluster�formation (Proof of Theorem 6)""; ""(c) Equilibrium fluctuations (Proof of Theorem 7)""

""(d) Mean�field continuum limit (Proof of Proposition 3.1 and Theorem 8)""

Notes:

"Volume 171, Number 809 (second of 4 numbers)."

Includes bibliographical references (p. 95-97).

Description based on print version record.

ISBN:

1-4704-0410-9