Quenched invariance principles for random walks in random environment conditioned to stay positive
报告专家：洪文明 教授（北京师范大学）
时间：9月23日（星期五）10:00-11:00
报告地点：腾讯会议：302-731-513 会议密码：0923
https://meeting.tencent.com/dm/dZnJTIVeShar
摘要：We consider a random walk $\{S_n\}_{n\in \mathbb{N}}$ in random environment (in time) $\xi$. For almost each realization of $\xi$, we prove a quenched invariance principles for the random walk conditioned to stay positive (which specified by the Doob $h$-transform of the original one). To this end, a key step is to formulate a (quenched) harmonic function. Although the traditional approach Wiener-Hopf factorisation dose not work in this case, we prove the existence of the (quenched) harmonic function under the annealed $2+\epsilon$ (for some $\epsilon>0$) moment condition on the increments. This is a joint work with Shengli Liang.
专家简介：洪文明，北京师范大学数学科学学院教授、博导，研究方向为概率论；主要研究兴趣包括随机环境中的随机游动，分枝过程及分枝随机游动等。在Electron. J. Probab., J. Theoret. Probab., Sci. China Math., Stochastic Process. Appl., Theory Probab. Appl., Markov Process. Related Fields, Infin. Dimens. Anal. Quantum Probab. Relat. Top.等重要杂志发表论文40多篇。
