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Jun
25
comment Logarithmic integral, $π(x)$ and $x/(\ln x)$
Not yet. See the discussion here: en.wikipedia.org/wiki/Skewes'_number#More_recent_estimates
Jun
25
comment Extrapolation between longest increasing and longest alternating subsequences
A trivial observation: there's some strange parity here. The Tracy widom distribution is biased toward one side, whereas the Gaussian is symmetric about the mean. This is evident here since for small $m$, we basically have reflection symmetry. So I would expect the transition to occur when $m\gg n/2$.
Jun
23
comment Semicircle law universality elsewhere
thanks for all your answers!
Jun
23
comment Bounds on the probability of k-of-n events in terms of bounds on single and pairwise probabilities
It sounds like you could really use something akin to positive/negative association such as $P(A_i\cap A_j)\leq \geq P(A_i)P(A_j)$. Do you happen to know if these hold on some large subset of index pairs?
Jun
22
revised Semicircle law universality elsewhere
added 4 characters in body
Jun
22
comment Why is this distribution exponential?
Try working this out with just two points.
Jun
22
comment Why is this distribution exponential?
Basically by rescaling the interval as a function of $n$ the waiting time between successive points becomes a poisson process. This is because the probability of seeing the next point is proportional to the interval you are looking at.
Jun
19
comment Semicircle law universality elsewhere
@jon bannon: I'm not intimately familiar with it but I basically lumped it with random matrix theory. If this is wrong of me I would love to see a note on this.
Jun
19
revised Semicircle law universality elsewhere
deleted 1 character in body
Jun
19
asked Semicircle law universality elsewhere
Jun
18
comment Determinant Evaluation
@SteveHuntsman: I have, for example "A determinental evaluation and some enumeration results for plane partitions": citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.3644 It seems like this essentially counts plane-partitions bounded by $c$. In the paper it's mentioned that there's no known explicit formula in the general case but I'm wondering if these have been considered elsewhere? In the linked paper, Theorem 5 has something similar but by a (intended) miracle, the calculation goes through.
Jun
18
revised Determinant Evaluation
added 88 characters in body
Jun
17
revised Determinant Evaluation
added 4 characters in body
Jun
17
asked Determinant Evaluation
May
19
asked Character sums over a fixed subset of skew tableaux
May
18
comment Young Tableau Box Correlations
@oferzeitouni: I'm familiar with the mentioned lozenge tiling results but unfortunately I'm not sure if they apply here. Specifically, lozenge tilings use Plancherel measure whereas this problem is for uniform measure on a fixed tableau. As well, as far as I remember, schur functions and macdonald polynomials index lozenge tile locations and don't really rely on exact single box distributions. The only connection I see to Plancherel measure is that the resulting square limit curves are in some sense deformed Logan-Shepp curves.
May
12
asked Young Tableau Box Correlations
May
2
awarded  Investor
Apr
2
awarded  Custodian
Apr
2
reviewed Approve What is the easiest randomized algorithm to motivate to the layperson?