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visits | member for | 5 years, 8 months |
seen | 1 hour ago | |
stats | profile views | 1,498 |
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? |