Infinite differentiability of the free energy for a Derrida-Retaux system

：陈新兴（上海交通大学）
：2024-08-21 10:00
：海韵园数理大楼686会议室

报告人：陈新兴（上海交通大学）

时  间：2024年8月21日10:00

地  点：海韵园数理大楼686会议室

内容摘要:

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.  

个人简介：

陈新兴，上海交通大学副教授。 2001年厦门大学本科毕业，2007年获得复旦大学理学博士学位，2007-2009年在北京大学从事博士后研究。主要研究兴趣为随机游动和随机图，已有多个成果发表在Ann. Probab., Probab. Theory Related Fields, Math. Ann., Sci. China Math. 等学术期刊。

 

联系人：陈娴