A number of continuous interacting particle systems can be described as collections of Brownian particles on the real line whose collision dynamics are mediated by the local times associated with the gaps between adjacent particles.  Examples of systems in this class include the ordered particle dynamics of rank-based diffusions and certain eigenvalue processes arising in…

The trace reconstruction problem asks to reconstruct an unknown n-bit string x given independent random "traces" of x, where a random trace is obtained by first deleting each bit of x independently with some probability (say 0.5), and then outputting the concatenation of the remaining bits of x. A basic question is to determine the…

Given a set K in R^2 with Hausdorff dimension t \in , what can we say about a typical orthogonal projection of K? Marstrand (1954) proved that for Lebesgue almost all unit vectors \theta \in S^1, the dimension of the projection \pi_\theta (K) to \theta is min{t, 1}. To refine the question, we can replace…

Speaker's website: https://www.stat.berkeley.edu/~vadicgor/