Gibbs Distribution and the Repairman Problem

Hassan Chetouani and Nikolaos Limnios ()
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Hassan Chetouani: Applied Mathematics Laboratory, Université de Technologie de Compiègne, Sorbonne University Alliance, 60203 Compiègne, France
Nikolaos Limnios: Applied Mathematics Laboratory, Université de Technologie de Compiègne, Sorbonne University Alliance, 60203 Compiègne, France

Mathematics, 2023, vol. 11, issue 19, 1-14

Abstract: In this paper, we obtain weak convergence results for a family of Gibbs measures depending on the parameter θ > 0 in the following form d P θ ( x ) = Z θ exp − H θ ( x ) / θ d Q ( x ) , where we show that the limit distribution is concentrated in the set of the global minima of the limit Gibbs potential. We also give an explicit calculus for the limit distribution. Here, we use the above as an alternative to Lyapunov’s function or to direct methods for stationary probability convergence and apply it to the repairman problem. Finally, we illustrate this method with a numerical example.

Keywords: Gibbs measure; Gibbs potential; Laplace’s method; weak convergence; repairman problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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