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Related lectures (30)

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Expected Number of Visits in State

Covers the criterion for recurrence in infinite chains based on the expected number of visits in a state.

Conformal Loop Ensembles: Perspectives and Applications

Covers conformal loop ensembles and their applications in conformal field theory and quantum gravity.

Markov Chains: Definition and Examples

Covers the definition and properties of Markov chains, including transition matrix and examples.

Diffusion in Crystals: Atomic Theory and Random Motion

Explores atomic theory of diffusion in crystals and random motion.

Martingales and Brownian Motion: Construction and Properties

Explores the construction and properties of a Brownian motion with continuous trajectories using Paul Lévy's method.

Doob's Decomposition Theorem

Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.

Random Field Ising Model

Covers the Random Field Ising Model, discussing the concept of disorder and the process of finding the ground state.

Luria-Delbrück Experiment

Explores the implications of the Luria-Delbrück experiment on evolutionary mechanisms and the importance of probabilities in understanding biological data.

Fluctuation-dissipation relations for reversible diffusions

Covers linear response, steady states, Girsanov transforms, and covariance limits in reversible diffusions.

Stochastic Differential Equations

Covers Stochastic Differential Equations, Wiener increment, Ito's lemma, and white noise integration in financial modeling.