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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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C. Douglas Howard                                 November 16, 2000
Department of Mathematics                         304 Whitehead Hall
Baruch College, City University of New York       Preseminar: 3:00 p.m.
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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              EUCLIDEAN MODELS OF FIRST-PASSAGE PERCOLATION


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                             ABSTRACT

First-passage percolation (FPP) was first introduced by Hammersley and
Welsh as a model of fluid flow through a randomly porous material.  In the
standard FPP model, the spatial randomness of the material is represented
by i.i.d. nonnegative random variables  tau(e)  indexed by the edges  e
of the  Z^d  nearest-neighbor lattice.  In contrast, in "Euclidean"
models of FPP (and in related models studied by Vahidi-Asl and Wierman and
later by Serafini), the material is represented by a homogeneous Poisson
point process.  In our models, roughly speaking, fluid flows through the
material faster in regions where the Poisson particles are closer together
and flows more slowly where they are relatively sparse.  This formulation
offers substantial technical advantages over lattice models, chiefly
flowing from the statistical invariance of particle configurations under
all rigid motions of  R^d.  We survey results known rigorously for
Euclidean FPP whose lattice analogs remain elusive.

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