Biomedical subjects

M Isopi

Publications and source records attributed to M Isopi.

2 recordsLinked to original sources

PubMed2002

The Brownian web.

Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab. Theory Relat. Fields 111, 375-452] constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from every space-time point. We extend their work by constructing and characterizing what we call the Brownian Web as a random variable taking values in an appropriate (metric) space whose points are (compact) sets of paths. This leads to general convergence criteria and, in particular, to convergence in distribution of coalescing random walks in the scaling limit to the Brownian Web.

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PubMed2001

Aging in 1D discrete spin models and equivalent systems.

We derive exact expressions for a number of aging functions that are scaling limits of nonequilibrium correlations, R(t(w),t(w)+t) as t(w)-->infinity, t/t(w)-->theta, in the 1D homogenous q-state Potts model for all q with T = 0 dynamics following a quench from T = infinity. One such quantity is (0)(t(w));sigma-->(n)(t(w)+t)> when n/square root of ([t(w))-->z. Exact, closed-form expressions are also obtained when an interlude of T = infinity dynamics occurs. Our derivations express the scaling limit via coalescing Brownian paths and a "Brownian space-time spanning tree," which also yields other aging functions, such as the persistence probability of no spin flip at 0 between t(w) and t(w)+t.

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