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Ben's Planet Posts

Central Limit Theorem

The central limit theorem is a cornerstone of statistics, stating that the sum of many random variables will be approximately normally distributed, and thereby explaining the ubiquity of the normal distribution. An example is the normal approximation of the Binomial…

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Random Variables

Usually, we are not only interested in the outcomes of a random experiment or combinations thereof, but also the implications they might have – which might be quantified by a value and brings us to the concept of a random…

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Lyapunov Exponents

Originally introduced by A. M. Lyapunov in 1892, Lyapunov exponents are a tool to quantify the characteristic sensitive dependence on initial conditions for chaotic dynamical systems. Let $\vec{x}(0)$ be the initial state of a chaotic dynamical system in phase space…

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Neural-Network Quantum States

Notes on a talk by Guiseppe Carleo given at the SCQM 2020 winter school. Describing a single spin-$\frac{1}{2}$ particle can be achieved by the simple ansatz $$| \psi \rangle = C_{\uparrow} |\uparrow\rangle + C_{\downarrow} | \downarrow\rangle$$ and the normalization condition…

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