On the finite size corrections to some random matching problems
G. Parisi, M. Ratieville
TL;DR
This paper revisits finite size corrections in random link matching problems, correcting previous errors in bipartite cases and extending analysis in non-bipartite cases, clarifying theoretical discrepancies.
Contribution
The paper corrects earlier mistakes in bipartite matching corrections and extends the analysis to non-bipartite cases, providing more accurate theoretical results.
Findings
Corrected finite size correction results for bipartite matching problems
Confirmed and extended results for non-bipartite matching problems
Resolved contradictions in previous theoretical work
Abstract
We get back to the computation of the leading finite size corrections to some random link matching problems, first adressed by Mezard and Parisi [J. Physique 48 (1987) 1451-1459]. In the so-called bipartite case, their result is in contradiction with subsequent works. We show that they made some mistakes, and correcting them, we get the expected result. In the non bipartite case, we agree with their result but push the analytical treatment further
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