When Harish-Chandra died in 1983, he left behind a voluminous pile of handwritten manuscripts on harmonic analysis on semisimple Lie groups over real/complex and p-adic fields. The manuscripts were turned over to the archives of the Institute for Advanced Study at Princeton, and are archived there. Robert Langlands is the Trustee of the Harish- Chandra archive, and has always been interested in finding a way of salvaging whatever might be valuable in these manuscripts. Some years ago, at a conference in UCLA, he asked if V. S. Varadarajan and I might look at some of these. The results of our efforts have resulted in the publication of the Volume 5 (Posthumous) of the Collected works of Harish-Chandra by Springer Verlag. My talk will be devoted to a bare outline of the results in this volume, without much detail, but I will try to convey some information about the key method used in the work.

We shall consider branching random walk with displacements having regularly varying tails. Extreme positions of particles are very important to study in the context of statistical physics, computer science, probability and biology. Point process is the best known tool in extreme value theory to study joint asymptotic behavior of extremes. In this talk, we shall focus on large deviation results for point processes arising in the above mentioned model.

The global distribution of $\nu_y(n)$, the number of (distinct) prime factors of $n$ which are $