AbstractIn this talk, we study some stochastic differential equations related to continuous measurements of open quantum systems. In these equations, we consider the regime where the coefficient on the noise tends to infinity. Under some conditions, we get pure jump processes which correspond to continuous time Markov chains, these processes being decorated with spikes distributed like a Poisso...
AbstractExtremal eigenvalues of graphs are of particular interest in theoretical computer science and combinatorics. Specifically, the spectral gap—the gap between the first and second largest eigenvalues—measures the expanding property of the graph. In this talk, I will focus on random $d$-regular graphs, for which the largest eigenvalue is $d$.I'll first explain some conjectures on the extr...