Speaker：Xinxing Chen (Shanghai Jiao Tong University)

Time：2024-8-21, 10:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

We consider a recursive system which was introduced by Derrida and Retaux (2014) as a toy model to study the depinning transition in presence of disorder. Derrida and Retaux predicted the free energy $F_\infty(p)$ of the system exhibit quite an unusual physical phenomenon which is an  infinite order phase transition. Hu and Shi (2018) studied a special situation and obtained other behavior of the free energy, while insisted on $p=p_c$ being an essential singularity. Recently, Chen, Dagard, Derrida, Hu, Lifshits and Shi (2021) confirmed the Derrida-Retaux conjecture under suitable integrability condition. However, from a mathematical point of view, it is still unknown whether the free energy is infinitely differentiable at the critical point. So that, we continue to study the infinite differentiability of the free energy in this paper.

References

[1] Derrida and Retaux (2014). The depinning transition in presence of disorder: a toy model. J. Statist. Phys. 156, 268-290.

[2] Hu and Shi (2018). The free energy in the Derrida–Retaux recursive model. J. Statist. Phys. 172, 718-741.

[3] Chen, X., Dagard, V., Derrida, B., Hu, Y., Lifshits, M. and Shi, Z. (2021). The Derrida-Retaux Conjecture on Recursive models, Ann. Probab., 49, 637-670.