Abstract:

The study of the conditioned limit theorems for random walks with independent and identically distributed jumps on the real line has been initiated by Spitzer and Feller and have attracted the interest of many authors in recent decades. The case of sums of dependent random variables is considerably less explored, mainly due to two challenges. The first one arises from the inapplicability of Wiener-Hopf factorization in this context. The second one is associated with the techniques of reversibility of the random walk, and the issue for dependent random variables is that, in general, the reversed random walk does not exhibit the same dependence structure as the direct random walk. In this talk, we present recent progress on conditioned local limit theorems for products of random matrices, and give potential applications of our results to the study of branching random walks on linear groups and multidimensional Mandelbrot cascades.

Speaker:

肖惠，中国科学院数学与系统科学研究院副研究员。主要研究兴趣为随机矩阵乘积和分枝随机游动等。相关论文发表在J. Eur. Math. Soc.，Ann. Probab.，Ergodic Theory Dynam. Systems，Ann. Inst. Henri Poincaré Probab. Stat.，Stochastic Process. Appl.，J. Differential Equations等。