Hi All, Just wanted to announce that we posted Jiahao's recent talk on our youtube page:
https://www.youtube.com/watch?v=68yy33jOkOs Thanks again to both Jiahao and Andreas for the great talks! Abstract: Free probability, random matrices and disorder in organic semiconductors Jiahao Chen, MIT CSAIL Random matrix theory has long been used to study the spectral properties of physical systems, and has led to a rich interplay between probability theory and physics [1]. Historically, random matrices have been used to model physical systems with random fluctuations, or systems whose eigenproblems were too difficult to solve numerically. This talk explores applications of RMT to the physics of disorder in organic semiconductors [2,3]. Revisiting the old problem of Anderson localization [4] has shed new light on the emerging field of free probability theory [5]. I will discuss the implications of free probabilistic ideas for finite-dimensional random matrices [6], as well as some hypotheses about eigenvector locality. Algorithms are available in the RandomMatrices.jl package [7] written for the Julia programming language. [1] M. L. Mehta. Random matrices, 3/e, Academic Press, 2000. [2] J. Chen, E. Hontz, J. Moix, M. Welborn, T. Van Voorhis, A. Suarez, R. Movassagh, and A. Edelman. Error analysis of free probability approximations to the density of states of disordered systems. Phys. Rev. Lett. (2012) 109:36403. [3] M. Welborn, J. Chen, and T. Van Voorhis. Densities of states for disordered systems from free probability. Phys. Rev. B (2013) 88:205113. [4] P. W. Anderson. Absence of diffusion in certain random lattices. Phys. Rev. (1958) 109:1492--1505. [5] D. Voiculescu. Addition of certain non-commuting random variables. J. Functional Anal. (1986) 66:323--346. [6] J. Chen, T. Van Voorhis, and A. Edelman. Partial freeness of random matrices. arXiv:1204.2257 [7] https://github.com/jiahao/RandomMatrices.jl
