Publication

Multiple Points Of The Brownian Sheet In Critical Dimensions

Robert Dalang
2015
Journal Articles

Abstract

It is well known that an N-parameter d-dimensional Brownian sheet has no k-multiple points when (k - 1)d > 2kN, and does have such points when (k - 1)d < 2kN. We complete the study of the existence of k-multiple points by showing that in the critical cases where (k - 1)d = 2kN, there are a.s. no k-multiple points.

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https://infoscience.epfl.ch/entities/publication/e6f3d3b8-8538-4d81-bf2e-76f6bfeba3c1

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Robert Dalang
2015
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/e6f3d3b8-8538-4d81-bf2e-76f6bfeba3c1

About this result

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Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on: the dimension of the system the range of the interaction the spin dimension These properties of critical exponents are supported by experimental data.

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