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A theorem of Michael Mürmann revisited

  • Stochastic Geometry
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Abstract

A fundamental theorem of Mürmann [2] characterizing equilibrium distributions of physical clusters is reconsidered. We recover this result by means of the integration by parts formula approach to Gibbs processes due to Nguyen Xuan Xanh and Hans Zessin [4].

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References

  1. J.-B. Gouéré, Existence of subcritical regimes in the Poisson Boolean model of continuum percolation. Preprint (2006).

  2. M. G. Mürmann, “Equilibrium distributions of physical clusters,” Comm. Math. Phys. 45, 233–246 (1975).

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  3. M. G. Mürmann, “Poisson point processes with exclusion,” Z. Wahrscheinlichkeitstheorie verw. Gebiete 43, 23–37 (1978).

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  4. X. X. Nguyen and H. Zessin, “Integral and differential characterizations of the Gibbs process,” Math. Nachr. 88, 105–115 (1979).

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  5. D. Ruelle, Statistical Mechanics (Benjamin, New York, 1969).

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Correspondence to H. Zessin.

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Dedicated to Reinhard Lang on the occasion of his 60 th birthday.

Original Russian Text © H. Zessin, 2008, published in Izvestiya NAN Armenii. Matematika, 2008, No. 1, pp. 62–74.

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Zessin, H. A theorem of Michael Mürmann revisited. J. Contemp. Mathemat. Anal. 43, 50–58 (2008). https://doi.org/10.3103/s11957-008-1004-y

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  • DOI: https://doi.org/10.3103/s11957-008-1004-y

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