Abstract
We study the asymptotic behaviour of a class of self-attracting motions on $\mathbb{R}^d$. We prove the decrease of the free energy related to the system and mix it together with stochastic approximation methods. We finally obtain the (limit-quotient) ergodicity of the self-attracting diffusion with a speed of convergence.
Citation
Victor Kleptsyn. Aline Kurtzmann. "Ergodicity of self-attracting motion." Electron. J. Probab. 17 1 - 37, 2012. https://doi.org/10.1214/EJP.v17-2121
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