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  • 1
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The inequalities for spin correlation functions of ferromagnetic Ising models with pair interactions derived in a previous paper are studied in more detail. It is shown that each of these inequalities is a positive linear combination of a finite number of “extremal” inequalities, which can in principle be determined and of which a number of examples is given.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove that increasing function on a finite distributive lattice are positively correlated by positive measures satisfying a suitable convexity property. Applications to Ising ferromagnets in an arbitrary magnetic field and to the random cluster model are given.
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  • 3
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract For Ising models with pair interactions in zero magnetic field a class of linear combinations of products of two correlation functions is studied. We derive sufficient and necessary conditions under which a function in this class is (a) zero for all values of the coupling parameters, or (b) nonnegative for all nonnegative values of the coupling parameters. Examples of correlation-function identities and inequalities of this type are given.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 30 (1983), S. 363-372 
    ISSN: 1572-9613
    Keywords: Random walks ; inhomogeneous lattice ; perfect and imperfect traps ; average number of steps until trapping ; probability of return to the origin ; FKG inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For lattices with two kinds of points (“black” and “white”), distributed according to a translation-invariant joint probability distribution, we study statistical properties of the sequence of consecutive colors encountered by a random walker moving through the lattice. The probability distribution for the single steps of the walk is considered to be independent of the colors of the points. Several exact results are presented which are valid in any number of dimensions and for arbitrary probability distributions for the coloring of the points and the steps of the walk. They are used to derive a few general properties of random walks on lattices containing traps.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 46 (1987), S. 811-827 
    ISSN: 1572-9613
    Keywords: Stationary stochastic process ; 0–1 process ; first-passage time ; recurrence time ; Poincaré cycle ; inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Mark Kac's theorem on the mean recurrence time in a stationary stochastic process in discrete time with discrete states is taken as the starting point for a series of variations, most of which are formulated in terms of 0–1 processes. Whereas the original theorem deals with the mean recurrence time of a given state under the condition that the state is realized at time 0, this condition is dropped in part of the variations; two others refer to the variance of the recurrence time and two to the Poincaré cycle of a dynamical system. Most variations consist in inequalities and formal identities for the mean first-arrival time and subsequent recurrence times for the given state.
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  • 6
    ISSN: 1572-9613
    Keywords: Random walks ; inhomogeneous lattice ; colored points ; average length of successive runs ; ergodic theorems ; perfect and imperfect traps
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We continue our investigation of a model of random walks on lattices with two kinds of points, “black” and “white.” The colors of the points are stochastic variables with a translation-invariant, but otherwise arbitrary, joint probability distribution. The steps of the random walk are independent of the colors. We are interested in the stochastic properties of the sequence of consecutive colors encountered by the walker. In this paper we first summarize and extend our earlier general results. Then, under the restriction that the random walk be symmetric, we derive a set of rigorous inequalities for the average length of the subwalk from the starting point to a first black point and of the subwalks between black points visited in succession. A remarkable difference in behavior is found between subwalks following an odd-numbered and subwalks following an evennumbered visit to a black point. The results can be applied to a trapping problem by identifying the black points with imperfect traps.
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