MathDB3 problems
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Invariance principle for random walks on discrete point processes
Brownian-motion conjecture. Under assumptions … , Theorem $$ can be strengthened so that the random walk on a discrete point process, under appropriate scaling, converges to Browni…
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Examples with a central limit theorem but infinite second moments
Infinite-second-moment examples conjecture. There exist random walks on discrete point processes that satisfy a Central Limit Theorem but do not have all of their second moments fi…
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The central limit theorem under finite second moments
Finite-second-moment conjecture. Theorem $$ remains true under the weaker assumption that only the second moments are finite.