Simple one-dimensional interaction systems with superexponential relaxation times |
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Authors: | Andrei Toom |
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Institution: | (1) Incarnate Word College, 78209 San Antonio, Texas |
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Abstract: | Finite one-dimensional random processes with local interaction are presented which keep some information of a topological nature about their initial conditions during time, the logarithm of whose expectation grows asymptotically at least asM
3, whereM is the size of the setR
M
of states of one component. ActuallyR
M
is a circle of lengthM. At every moment of the discrete time every component turns into some kind of average of its neighbors, after which it makes a random step along this circle. All these steps are mutually independent and identically distributed. In the present version the absolute values of the steps never exceed a constant. The processes are uniform in space, time, and the set of states. This estimation contributes to our awareness of what kind of stable behavior one can expect from one-dimensional random processes with local interaction.Partially supported by NSF grant #DMS-932 1216. |
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Keywords: | Random processes one-dimensional local interaction relaxation time smoothing Cramé r-Edgeworth expansion harnesses |
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