Speaker : | Kavitha Veeraruna |

IIT Bombay | |

Date: | 13/12/2017 |

Time: | 2:00 pm - 3:00 pm |

Location: | Doctoral Training Center (EIT Digital) |

### Abstract

Abstract: We consider vector fixed point (FP) equations in large

dimensional spaces involving random variables, and study their

realization-wise solutions. We have an underlying directed random

graph, that defines the connections between various components of the

FP equations. Existence of an edge between nodes i,j implies the i-th

FP equation depends on the j-th component. We consider a special case

where any component of the FP equation depends upon an appropriate

aggregate of that of the random “neighbor” components. We obtain

finite dimensional limit FP equations (in a much smaller dimensional

space), whose solutions approximate the solution of the random FP

equations for almost all realizations, in the asymptotic limit (number

of components increase). Our techniques are different from the

traditional mean-field methods, which deal with stochastic FP equations

in the space of distributions to describe the stationary distributions

of the systems. In contrast our focus is on realization-wise FP

solutions. We apply the results to study systemic risk in a large

financial heterogeneous network with many small institutions and one

big institution, and demonstrate some interesting phenomenon.

Biography: Kavitha Veeraruna completed my PhD with Indian Institute of

Science in 2007. I have done two postdocs, one at TIFR Bangalore and

then with Prof. Eitan Altman at INRIA. Currently I am working as an

Assistant Professor at IIT Bombay Mumbai.