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Results tagged with big-list
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user 9564
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
76
votes
Ingenuity in mathematics
"At any party, there are at least two people with the same number of friends there".
This typically won't be obvious to someone who isn't a mathematician. However, it's quite easy for many people to …
-1
votes
Interesting examples of generic behavior of mathematical objects being either unreasonably s...
Given the initial state (assumed not to be at the origin) of a Brownian motion in $\mathbb{R}^2$, and the angular component of the process in polar coordinates, one can deduce the entire trajectory of …
7
votes
Random versions of deterministic problems
Neudecker and Williams proved that an analogue of the Riemann hypothesis holds with probability one for numbers drawn from a randomised version of the sieve of Eratosthenes.
2
votes
Seemingly emergent structures in mathematics
Thurston's geometrisation conjecture might be a good example here. If you start with a few simple 3-manifolds, you can combine them to create any 3-manifold you want.
3
votes
Dimension leaps
Brownian motion is recurrent in dimensions 1 and 2, and transient in three or more dimensions.
5
votes
Trichotomies in mathematics
Every logical statement is either true, undecidable or false.
2
votes
What results would follow from or imply "randomness" of the primes?
Billingsley wrote a nice article on the relationship between numbers, random walks and Brownian motion.
0
votes
Brownian motion, martingales, Markov Chains - Rosetta Stone
If X is a continuous martingale of finite variation such that $X_0 = 0$, then $P(X_t = 0 \ \ \forall t) = 1$.
2
votes
Brownian motion, martingales, Markov Chains - Rosetta Stone
Levy's characterisation of Brownian motion:
If $X$ is a continuous martingale and $X$ has quadratic variation process $[ X ]_t = t$ then $X$ is a standard Brownian motion.