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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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The Euclidean Matching Problem (Hardcover, 1st ed. 2017)
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The Euclidean Matching Problem (Hardcover, 1st ed. 2017)
Series: Springer Theses
Expected to ship within 18 - 22 working days
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This thesis discusses the random Euclidean bipartite matching
problem, i.e., the matching problem between two different sets of
points randomly generated on the Euclidean domain. The presence of
both randomness and Euclidean constraints makes the study of the
average properties of the solution highly relevant. The thesis
reviews a number of known results about both matching problems and
Euclidean matching problems. It then goes on to provide a complete
and general solution for the one dimensional problem in the case of
convex cost functionals and, moreover, discusses a potential
approach to the average optimal matching cost and its finite size
corrections in the quadratic case. The correlation functions of the
optimal matching map in the thermodynamical limit are also
analyzed. Lastly, using a functional approach, the thesis puts
forward a general recipe for the computation of the correlation
function of the optimal matching in any dimension and in a generic
domain.
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