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Large deviation principles for Euclidean functionals and other nearly additive processes
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  • Published: July 2001

Large deviation principles for Euclidean functionals and other nearly additive processes

  • Timo Seppäläinen1 &
  • J.E. Yukich2 

Probability Theory and Related Fields volume 120, pages 309–345 (2001)Cite this article

  • 205 Accesses

  • 14 Citations

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Abstract.

We prove a large deviation principle for a process indexed by cubes of the multidimensional integer lattice or Euclidean space, under approximate additivity and regularity hypotheses. The rate function is the convex dual of the limiting logarithmic moment generating function. In some applications the rate function can be expressed in terms of relative entropy. The general result applies to processes in Euclidean combinatorial optimization, statistical mechanics, and computational geometry. Examples include the length of the minimal tour (the traveling salesman problem), the length of the minimal matching graph, the length of the minimal spanning tree, the length of the k-nearest neighbors graph, and the free energy of a short-range spin glass model.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA. e-mail: seppalai@iastate.edu, , , , , , US

    Timo Seppäläinen

  2. Department of Mathematics, Lehigh University, 14 E. Packer Avenue, Bethlehem, PA 18015-3174, USA. e-mail: joseph.yukich@lehigh.edu, , , , , , US

    J.E. Yukich

Authors
  1. Timo Seppäläinen
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  2. J.E. Yukich
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Additional information

Received: 3 April 1999 / Revised version: 23 June 1999 / Published online: 8 May 2001

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Seppäläinen, T., Yukich, J. Large deviation principles for Euclidean functionals and other nearly additive processes. Probab Theory Relat Fields 120, 309–345 (2001). https://doi.org/10.1007/PL00008785

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  • Issue Date: July 2001

  • DOI: https://doi.org/10.1007/PL00008785

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  • Mathematics Subject Classification (2000): 60F10, 05C80, 60D05
  • Key words or phrases: Large deviation principles – Random graphs – Combinatorial optimization – Statistical mechanics – Spin glass model
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