Christoph Börgers
Department of Mathematics,
Tufts University
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Archived Blog Posts
Abel summability
Abel’s theorem
Acceptance-rejection sampling from a Gaussian distribution
Acceptance-rejection sampling from a heavy-tailed distribution
Algebras of sets and finitely additive measures
Analyticity of the Laplace transform
Approximating L1-functions by smooth functions
Arctangent at infinity
Asymptotic results motivated by Abel’s theorem
Bayes’ theorem
Binomial series
Bohr-Mollerup Theorem
Borel-Cantelli lemma
Brownian motion
Brownian motion and diffusion
Cadlag property of distribution functions
Caratheodory measurable sets
Caratheodory outer measure
Caratheodory's extension theorem
Caratheodory's sigma algebra versus the generated sigma algebra
Cauchy's formula for repeated anti-differentiation
Characteristic functions of Borel probability measures
Convergence almost surely, in probability, and in distribution
Convergence in distribution
Dynkin's pi-lambda theorem
Equilibrium renewal processes, non-rigorous treatment
Error function
Euler's product representation of the gamma function
Euler-Mascheroni constant
Expected value
Exponential integral
Extendability condition for finitely additive measures
Extendability condition for the Stieltjes length of intervals
First passage times for Brownian motion in one dimension
First passage times for the simple random walk on the integers
Fourier transform of L1 functions
Frechet distributions
Gumbel distribution
Hegselmann-Krause model
Infinite products of positive numbers
Injectivity of the Laplace transform
Kermack-McKendrick model
Laplace transform, definition and examples
Law of exponents
Multivariate Gaussians
Pairwise comparison diagrams and preference schedules
Probability from evidence - Laplace’s rule of succession
Range voting and majority judgment
Rate of convergence to the Frechet limit, example 1
Rate of convergence to the Frechet limit, example 2
Rate of convergence to the Gumbel limit, example
Relativistic velocity addition from the constant of c
Riemann-Liouville fractional anti-derivative
Sampling from a convex combination of probability distributions
Shannon entropy
Symmetric random walks at constant speed on the real line
Tauber's theorem
Uniform convergence of distribution functions
Weibull distributions
What makes Tauber's theorem interesting?
When Ax and Bx have the same length for all x