Geodesic
Monotone nonincreasing random fields on posets. I
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IX, Tome 301 (2003), pp. 92-143 Cet article a éte moissonné depuis la source Math-Net.Ru

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For an arbitrary poset $H$ and measure $\rho$ on $H\times{\mathbf R}$ (where $\mathbf R$ is the real axis), we construct a monotone decreasing stochastic field $\eta_\rho$ and calculate finite-dimensional distributions of the field. In the case where $H$ is a $\wedge$-semilattice and the measure $\rho$ satisfies additional conditions, we calculate characteristics of the field $\eta_\rho$ such as the expectation of the field value at a point, variance of the field value at a point, and correlation function of the field. The described construction for random fields gives a new method for constructing positively defined functions on posets. 
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     title = {Monotone nonincreasing random fields on {posets.~I}},
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L. B. Beinenson. Monotone nonincreasing random fields on posets. I. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IX, Tome 301 (2003), pp. 92-143. http://geodesic.mathdoc.fr/item/ZNSL_2003_301_a2/

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