The Free Energy in the Derrida–Retaux Recursive Model
We are interested in a simple max-type recursive model studied by Derrida and Retaux (J Stat Phys 156:268–290, 2014) in the context of a physics problem, and find a wide range for the exponent in the free energy in the nearly supercritical regime.
KeywordsMax-type recursive model Free energy Multi-scale analysis
Mathematics Subject Classification60J80 82B44
We are grateful to Bernard Derrida who introduced us to the problem, and with whom we have had regular discussions for two years. We wish to thank Nina Gantert for many discussions, Quentin Berger for enlightenment on renormalisation models, and Chunhua Ma, Bastien Mallein and Quan Shi for pointing out  to us. Two anonymous referees have carefully read the manuscript; their insightful comments have led to improvements in the paper. The project was partly supported by ANR MALIN (ANR-16-CE93-0003); Y.H. also acknowledges support from ANR SWiWS (ANR-17-CE40-0032).
- 9.den Hollander, F.: Random Polymers. École d’Été de Probabilités de Saint-Flour XXXVII. Lecture Notes in Mathematics, vol. 1974. Springer, Berlin (2009)Google Scholar
- 16.Giacomin, G.: Disorder and Critical Phenomena Through Basic Probability Models. École d’Été de Probabilités de Saint-Flour XL. Lecture Notes in Mathematics, vol. 2025. Springer, Berlin (2011)Google Scholar
- 20.Goldschmidt, C., Przykucki, M.: Parking on a random tree (2016). arXiv:1610.08786
- 24.Lerouvillois, V.: Polymer pinning models and condition on the existence of a phase transition. Preprint (2015)Google Scholar
- 27.Monthus, C.: Strong disorder renewal approach to DNA denaturation and wetting: typical and large deviation properties of the free energy (2016). arXiv:1611.00501
- 29.Shi, Z.: Branching Random Walks. École d’été Saint-Flour XLII (2012). Lecture Notes in Mathematics, vol. 2151. Springer, Berlin (2015)Google Scholar