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Part of what I do is study typical behavior of large combinatorial structures by looking at pseudorandom instances. But many commercially available pseudorandom number generators have known defects, …

The $2m$th moment of the (random) area of the triangle whose vertices are three independent, uniformly distributed random points on the unit circle appears to be $((3m)!/(m!)^3)/16^m$. Can anyone prov …

What are the feasible $2^n$-tuples of entropies $h(S) := H(X_{i_1},\dots,X_{i_{|S|}})$ where $X_1,\dots,X_n$ are discrete random variables with some (unknown) joint probability distribution as $S=\{i_ …

How many steps on average does a simple random walk in the plane take before it visits a vertex it's visited before? If an exact formula does not exist (as seems likely), then I'm interested in good …

In the case where $\sum_{n \in \mathbb{Z}} \mu(n) = \sum_{n \in \mathbb{Z}} \nu(n) = 1$, this setup is reminiscent of the theory of martingales, so I'm tagging this question pr.probability as well as co.combinatorics …

Consider a disk of radius $r$ centered at $(x,y)$, where $(x,y)$ is chosen from the uniform distribution on $[0,1) \times [0,1)$, and let the random variable $N$ be the number of lattice points in the …

I've thought of an approach to variance reduction that surely can't be new, but I haven't been able to find it published anywhere; I'd appreciate some leads. Consider some sort of random variable $X$ …

In diffusion-limited aggregation on the square lattice, one lets a particle do "random walk from infinity" until it hits the current aggregate, at which point the site occupied by the particle is adde …

Can anyone suggest a simple and efficient way (preferably embodied in computer code) to compute the average height function for lozenge tilings of an $a,b,c,a,b,c$ semiregular hexagon? I prefer to sc …

Consider critical edge-percolation in the induced subgraph of the square grid with vertex set {$(i,j) \in Z \times Z:\ i+j \geq 0$}, and let $p_n$ be the probability that the cluster containing $(0,0) …

Where can I find a detailed write-up of the asymptotic shape of a $q$-weighted Young diagram inside an $a$-by-$b$ box, especially one that uses a variational approach? Equivalently, we can look at pr …

Let $X_1,X_2,\dots$ be iid draws from the uniform distribution on $\{1,2,...,m\}$, and let the random variable $N$ be the minimum $j$ such that $X_j = X_i$ for some $i<j$. I'm aware that the expected …

More than one combinator(ial?)ist has asked me to recommend a good book to learn probability from, and I never know what to say; the probability theory that I use in my research up was mostly learned …

Given two Markov chains with respective state-spaces $S$ and $T$, say that a function $\phi$ from $S$ to $T$ is holomorphic iff for all states $t \in T$, every real-valued function $f$ on $T$ that is …

In the case where $\sum_{n \in \mathbb{Z}} \mu(n) = \sum_{n \in \mathbb{Z}} \nu(n) = 1$, this setup is reminiscent of the theory of martingales, so I'm tagging this question pr.probability as well as co.combinatorics …