PhD Defense Tom Bannink
On January 30th Tom Bannink will defend his PhD thesis entitled 'Quantum and stochastic processes'.
Tom's promotors are Harry Buhrman and Frank den Hollander.
The PhD defense will take place in the Agnietenkapel (Oudezijds Voorburgwal 229 - 231, 1012 EZ Amsterdam) and will start at 10:00 hrs.
Tom has started as a deep learning scientisct at Plumerai, studying binarized neural networks.
In this dissertation we present results for various quantum and stochastic processes. First, we bound separations between the entangled and classical values for several classes of nonlocal t-player games. We show that for many general classes of such games, the entangled winning probability can not be much higher than the classical one. The proofs use semidefinite-programming techniques and hypergraph norms. Next, we study so-called quasirandom properties of graphs, and extend this to the quantum realm. For a certain class of quantum channels, we generalize several results on equivalence between different quasirandom properties, using the non-commutative Grothendieck inequality. We then continue by looking at methods for sampling random graphs with power-law degree distributions, using Markov Chain switching methods. Using these random samples we present a conjecture on the asymptotic number of triangles in the uniform random graph model. Next we study a class of stochastic processes on graphs that include the discrete Bak-Sneppen process and the contact process. These processes exhibit a phenomenon which we call the Power Light Cone, that has been used in the physics community for a long time but had not yet been proven. We provide a proof of this, which allows for numerical computations that can be used to estimate critical exponents. Finally we consider a quantum version of Pascal's triangle. When Pascal's triangle is plotted modulo 2, the Sierpinski triangle appears. We prove that when the quantum version of this triangle is plotted modulo 3, a fractal known as the Sierpinski carpet emerges.