#### DMCA

## A proof of Parisi’s conjecture on the random assignment problem (2003)

Venue: | PROBAB. THEORY RELAT. FIELDS |

Citations: | 48 - 17 self |

### Citations

92 | On the value of a random minimum spanning tree problem - Frieze - 1985 |

69 | On the solution of the random link matching problems - Mézard, Parisi - 1987 |

55 | The ζ(2) limit in the random assignment problem
- Aldous
(Show Context)
Citation Context ...W00] that the cover formula implies that the limit value of a standard square RAP with zeros outside an inscribed circle is equal to π2 /24. A result presented as a conjecture in [O92], and proved in =-=[A01]-=-, states that in the case k = m = n with no zeros, as n → ∞, the probability that the smallest element in a row belongs to the optimal assignment converges to 1/2. We can now give an exact formula for... |

51 | Constructive Bounds and Exact Expectations For the Random
- Coppersmith, Sorkin
- 1999
(Show Context)
Citation Context ...t exponential random variables with intensity 1. Then E(P) = 1 + 1 1 1 + + · · · + 4 9 k2. We also prove the following two generalizations. Theorem 1.2 (Conjectured by D. Coppersmith and G. B. Sorkin =-=[CS98]-=-). Let P be an RAP where the matrix entries are independent exponential random variables with intensity 1. Then (1) E(P) = � Date: 1st February 2008. i+j<k 1 (m − i)(n − j) . 1s2 SVANTE LINUSSON AND J... |

40 | Asymptotics in the random assignment problem - Aldous - 1992 |

37 | An upper bound on the expected cost of an optimal assignment - Karp - 1987 |

37 | On the expected value of a random assignment problem - Walkup - 1979 |

31 |
Asymptotic properties of the random assignment problem
- Olin
- 1992
(Show Context)
Citation Context ...lar it is shown in [LW00] that the cover formula implies that the limit value of a standard square RAP with zeros outside an inscribed circle is equal to π2 /24. A result presented as a conjecture in =-=[O92]-=-, and proved in [A01], states that in the case k = m = n with no zeros, as n → ∞, the probability that the smallest element in a row belongs to the optimal assignment converges to 1/2. We can now give... |

21 | Certain expected values in the random assignment problem - Lazarus - 1990 |

19 | Exact expectations and distributions in the random assignment problem - Alm, Sorkin |

19 |
A conjecture on random bipartite matching, Physics e-Print archive, http:// xxx.lang.gov/ps/cond-mat/9801176
- Parisi
- 1998
(Show Context)
Citation Context ...random assignment problem, we denote by E(P) the expected value of the minimal sum of an independent set of k matrix elements. In this article we prove the following. Theorem 1.1 (Parisi’s Conjecture =-=[P98]-=-). Let P be the RAP where k = m = n and the matrix entries are independent exponential random variables with intensity 1. Then E(P) = 1 + 1 1 1 + + · · · + 4 9 k2. We also prove the following two gene... |

17 | A lower bound on the expected cost of an optimal assignment - Goemans, Kodialam - 1993 |

14 | Algorithm and average-value bounds for assignment problems - Donath - 1969 |

14 | On the expected optimal value of random assignment problems: Experimental results and open questions - Pardalos, Ramakrishnan - 1993 |

13 | On the expected value of the minimum assignment, Random Structures Algorithms 21 - Buck, Chan, et al. |

12 | On the expected incremental cost of a minimum assignment - Coppersmith, Sorkin |

12 | 2003) A Proof of the Conjecture due to Parisi for the Finite Random Assignment Problem, Working Paper - Nair, Prabhakar, et al. |

9 | A generalization of the random assignment problem
- Linusson, Wästlund
- 2000
(Show Context)
Citation Context ...s are independent exponential random variables with intensity 1. Then (1) E(P) = � Date: 1st February 2008. i+j<k 1 (m − i)(n − j) . 1s2 SVANTE LINUSSON AND JOHAN WÄSTLUND Theorem 1.3 (Conjectured in =-=[LW00]-=-). Let P be an RAP where some matrix entries are zero and all the other entries are independent exponential random variables with intensity 1. Then (2) E(P) = 1 mn � i,j di,j(P) �m−1��n−1 i j where di... |

4 | Exact expectations for random graphs and assignments - Eriksson, Eriksson, et al. |

3 | On the value of a random minimum spanning tree - Frieze - 1985 |

2 | McDarmid Colin J.H., On random minimum spanning trees, Combinatorica 9 - Frieze - 1989 |

1 | McDarmid Colin J.H.: Random minimum length spanning trees in regular graphs - Beveridge, Frieze - 1998 |

1 | Nair, C.: Towards the resolution of Coppersmith-Sorkin conjectures - Lett - 1987 |