9-11 July 2018
Ho Chi Minh City University of Science
Asia/Ho_Chi_Minh timezone

Conditioned limit theorems for products of positive random matrices

10 Jul 2018, 14:00
30m
Ho Chi Minh City University of Science

Ho Chi Minh City University of Science

227 Nguyễn Văn Cừ, Phường 4, T.P. Hồ Chí Minh

Speaker

Dr Thi Da Cam PHAM (Institut Denis Poisson, Faculté des sciences, Tours, France.)

Description

Inspired by a recent paper of I. Grama, E. Le Page and M. Peigné, we consider a sequence $(g_n)_{n \geq 1}$ of i.i.d. random $d \times d -$ matrices with non negative entries and study the fluctuations of the process $(\log | g_n ... g_1 x ) {n \geq 1}$ for any non-zero vector $x$ in $R^d$ with non-negative coordinates. Our method involves approximating this process by a martingale and studying harmonic functions for its restriction to the upper half line. Under certain conditions, the probability for this process to stay in the upper half real line up to time $n$ decreases as $c \over \sqrt n$ for some positive constant $c$.

Primary author

Dr Thi Da Cam PHAM (Institut Denis Poisson, Faculté des sciences, Tours, France.)

Presentation Materials

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