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References
- H. Bauke, S. Franz, S. Mertens. Number partitioning as random energy model. Journal of Stat. Mech. : Theory and Experiment, page P04003 (2004).
- H. Bauke, S. Mertens. Universality in the level statistics of disordered systems. Phys. Rev. E 70, 025102(R) (2004).
- G. Ben Arous, V. Gayrard, A. Kuptsov. A new REM conjecture. Preprint (2006).
- Bolthausen, Erwin. A note on the diffusion of directed polymers in a random environment. Comm. Math. Phys. 123 (1989), no. 4, 529--534. MR1006293 (91a:60270)
- Borgs, Christian; Chayes, Jennifer; Pittel, Boris. Phase transition and finite-size scaling for the integer partitioning problem.Analysis of algorithms (Krynica Morska, 2000). Random Structures Algorithms 19 (2001), no. 3-4, 247--288. MR1871556 (2002j:90061)
- C. Borgs, J. Chayes, S. Mertens and C. Nair. Proof of the local REM conjecture for number partitioning I: Constant energy scales. Preprint (2005). To appear in Random Structures and Algorithms
- C. Borgs, J. Chayes, S. Mertens and C. Nair. Proof of the local REM conjecture for number partitioning II: Growing energy scales. Preprint (2005). To appear in Random Structures and Algorithms
- Borgs, C.; Chayes, J. T.; Mertens, S.; Pittel, B. Phase diagram for the constrained integer partitioning problem. Random Structures Algorithms 24 (2004), no. 3, 315--380. MR2068872 (2005c:82030)
- Bovier, Anton; Kurkova, Irina. Poisson convergence in the restricted $k$-partitioning problem. Random Structures Algorithms 30 (2007), no. 4, 505--531. MR2326156
- Bovier, Anton; Kurkova, Irina. Local energy statistics in disordered systems: a proof of the local REM conjecture. Comm. Math. Phys. 263 (2006), no. 2, 513--533. MR2207653 (2007b:82027)
- A. Bovier, I. Kurkova. A tomography of the GREM : beyond the REM conjecture. Commun. Math. Phys. 263 535--552 (2006).
- Comets, Francis; Shiga, Tokuzo; Yoshida, Nobuo. Probabilistic analysis of directed polymers in a random environment: a review. Stochastic analysis on large scale interacting systems, 115--142, Adv. Stud. Pure Math., 39, Math. Soc. Japan, Tokyo, 2004. MR2073332 (2005d:82050)
- Derrida, Bernard. Random-energy model: an exactly solvable model of disordered systems. Phys. Rev. B (3) 24 (1981), no. 5, 2613--2626. MR0627810 (83a:82018)
- B. Derrida. A generalisaton of the random energy model that incldes correlations betwen energies. Jounal Phys. Lett. 46, 401--407(1985).
- Erdös, P.; Taylor, S. J. Some problems concerning the structure of random walk paths. Acta Math. Acad. Sci. Hungar. 11 1960 137--162. (unbound insert). MR0121870 (22 #12599)
- Feller, William. An introduction to probability theory and its applications. Vol. I.Third edition John Wiley & Sons, Inc., New York-London-Sydney 1968 xviii+509 pp. MR0228020 (37 #3604)
- D.A. Huse, C.L. Henley. Pinning and roughening of domain wall in Ising systems due to random impurities, Phys. Rev. Lett. 54, 2708--2711 (1985)
- Imbrie, J. Z.; Spencer, T. Diffusion of directed polymers in a random environment. J. Statist. Phys. 52 (1988), no. 3-4, 609--626. MR0968950 (90m:60122)
- H. Krug, H. Spohn. Kinetic roughening of growing interfaces. In: Solids Far from Equilibrium, C. Godr\`eche ed., Cambridge University Press (1991).
- Mertens, Stephan. Phase transition in the number partitioning problem. Phys. Rev. Lett. 81 (1998), no. 20, 4281--4284. MR1653530 (99g:68097)
- Mertens, Stephan. A physicist's approach to number partitioning.Phase transitions in combinatorial problems (Trieste, 1999). Theoret. Comput. Sci. 265 (2001), no. 1-2, 79--108. MR1848213 (2003j:68068)

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