5 citations · 12 across the 6 of their papers we have counts for
6 papers
Entropic exercises around the Kneser-Poulsen conjecture
Gautam Aishwarya, Irfan Alam, Dongbin Li +2
We develop an information-theoretic approach to study the Kneser--Poulsen conjecture in discrete geometry. This leads us to a broad question regarding whether Rényi entropies of in…
Generalizing the de Finetti--Hewitt--Savage theorem
Irfan Alam
A sequence of random variables is called \textit{exchangeable} if its joint distribution is invariant under permutations of indices. The original formulation of de Finetti's theore…
A nonstandard proof of de Finetti's theorem
Irfan Alam
We give a nonstandard analytic proof of de Finetti's theorem for an exchangeable sequence of Bernoulli random variables. The theorem postulates that such a sequence is uniquely rep…
An introduction to the probabilistic method through the Lovász Local Lemma
Irfan Alam
We illustrate the use of probability theory in existential proofs, focusing on the Lovász Local Lemma. This result gives a lower bound for the probability of avoiding a suitable fi…
Limiting spherical integrals of bounded continuous functions
Irfan Alam
We use nonstandard analysis to study the problem of expressing a Gaussian integral in terms of the limiting behavior of a sequence of spherical integrals. Peterson and Sengupta pro…
Limiting Probability Measures
Irfan Alam
The coordinates along any fixed direction(s), of points on the sphere , roughly follow a standard Gaussian distribution as approaches infinity. We revisit th…