Mathematics · Core
Law of Large Numbers
The law of large numbers says the sample average converges to the expected value as n grows — the reason insurance and a large independent bet-set work, and a small correlated book does not.
Definition
Weak LLN: X̄ →_p μ. Strong LLN: almost-sure convergence under milder moment conditions. Both need some independence or weak dependence. Correlation across names kills the effective n.
Why it matters
‘We have 200 positions so we are diversified’ is an LLN claim. If they share one factor, n_eff ≈ 1.
Case
A book of 80 merger deals with the same funding and the same rate shock is not 80 independent Bernoulli trials.
How to read it
Estimate effective sample size after clustering. If n_eff is 8, you do not have an LLN yet.
No query has been run yet. Which is tragically normal for most knowledge systems, but we are trying to evolve past decorative databases.