André Toom | University of the Incarnate World - Estados Unidos

• Grant number: 97/06493-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 18, 1997
• End date: August 17, 1998
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics
• Principal Investigator: Pablo Augusto Ferrari
• Grantee: Pablo Augusto Ferrari
• Visiting researcher: André Toom
• Visiting researcher institution: University of the Incarnate Word, United States
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 95/00790-1 - Critical Phenomena are Present in Many Situations in Different Areas, AP.TEM

Abstract

Random processes with local interaction, existence and properties of their invariant distributions and their asymptotic behavior will be studied. Particular attention will be devoted to two special topics: (a) spontaneous symmetry breaking and (b) mathematical models of interfaces with linear interaction. In (a), we will investigate certain models that seem to contradict to the common belief that the spontaneous symmetry breaking does not exist in one-dimensional models. In (b), we will investigate the processes that model crystallic structures (Hammersley's harnesses) and sandpiles (Edwards & Wilkinson's equation). These studies are relevant to problems of dynamic scaling, fractal surfaces and percolation networks. (AU)