List of probabilistic proofs of non-probabilistic theorems

Probability theory routinely uses results from other fields of mathematics (mostly, analysis). The opposite cases, collected below, are relatively rare; however, probability theory is used systematically in combinatorics via the probabilistic method. They are particularly used for non-constructive proofs.

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enProbability theory routinely uses results from other fields of mathematics (mostly, analysis). The opposite cases, collected below, are relatively rare; however, probability theory is used systematically in combinatorics via the probabilistic method. They are particularly used for non-constructive proofs.
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enProbability theory routinely uses results from other fields of mathematics (mostly, analysis). The opposite cases, collected below, are relatively rare; however, probability theory is used systematically in combinatorics via the probabilistic method. They are particularly used for non-constructive proofs.
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List of probabilistic proofs of non-probabilistic theorems
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enList of probabilistic proofs of non-probabilistic theorems
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Abraham de Moivre
Atiyah–Singer index theorem
Banach–Mazur compactum
Basel problem
Bell inequalities
Bernstein polynomial
Boundary (topology)
Boundary Harnack principle
Brownian motion
Category:Mathematical proofs
Category:Probabilistic arguments
Channel capacity
Claude Shannon
Combinatorics
Compact surface
Computable number
Coupling
Coupling (probability)
Crossing number inequality
Doob's martingale convergence theorems
Dvoretzky's theorem
Émile Borel
Fundamental theorem of algebra
Harmonic function
Hausdorff–Young inequality
Holomorphic function
Introduction to systolic geometry
Ivan Privalov
Law of large numbers
Lipschitz function
Local time (mathematics)
Loewner's torus inequality
Markov chain
Martin boundary
Martingale convergence
MathOverflow
Maximum-minimums identity
Minimal surface
Noisy-channel coding theorem
Non-constructive
Normal number
Picard theorem
Probabilistic method
Probability theory
Random compact set
Rogers–Ramanujan identities
Stirling's formula
Stochastic calculus
Strong law of large numbers
Tensor product of Hilbert spaces
The Doctrine of Chances
Variance
Von Neumann algebra
Weak law of large numbers
Weierstrass approximation theorem
Weierstrass function
Wiener process
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Q7246862
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Category:Mathematical proofs
Category:Probabilistic arguments
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