Award Abstract #9803140
Markov Processes

NSF Org:	DMS Division of Mathematical Sciences
Initial Amendment Date:	May 22, 1998
Latest Amendment Date:	April 14, 2000
Award Number:	9803140
Award Instrument:	Continuing grant
Program Manager:	Keith N. Crank DMS Division of Mathematical Sciences MPS Directorate for Mathematical & Physical Sciences
Start Date:	June 1, 1998
Expires:	May 31, 2002 (Estimated)
Awarded Amount to Date:	$350948
Investigator(s):	Srinivasa Varadhan varadhan@cims.nyu.edu (Principal Investigator)
Sponsor:	New York University 70 WASHINGTON SQUARE S NEW YORK, NY 10012 212/998-2121
NSF Program(s):	PROBABILITY
Field Application(s):	0000099 Other Applications NEC
Program Reference Code(s):	OTHR,0000
Program Element Code(s):	1263

ABSTRACT

9803140

Varadhan

In this project the investigator will study the behavior of complex interactive

systems with conserved quantities. Their evolution is often described at the microscopic level while questions are asked at a much larger or macroscopic scale. The transition from one scale to another always requires some averaging at the microscopic level and sometimes, as in the non gradient models, getting rid of certain divergences as well. In the case of hyperbolic scaling, the macroscopic equation is a nonlinear hyperbolic equation that develops shocks. The characterization of the microscopic profile of the shock is an interesting problem. Studying the rescaled motion of a single tagged particle that interacts with large number of particles requires a central limit theorem to be proved under very minimal mixing assumptions.

Many complex physical systems consist of a large number of elementary components. Each of these components interacts in some fashion only with a few neighboring ones. However, the large system, as a whole, evolves in some complex manner due to the interactions of the individual components. This project is devoted to the exploration of this phenomenon, in several concrete examples. The goal is to provide mechanisms for making inferences about the behavior in the large scale based on assumptions on the nature of the interaction in the small scale.

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