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The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.

2 votes
1 answer
126 views

Are the eigenvalues of the 1D lattice with random weights known?

Consider the adjacency matrix $\mathbf{A}$ of a one dimensional lattice of size $N$. That is, $A$ is a $N\times N$ matrix with $A_{ij}=1$ if vertex $i$ adjacent to vertex $j$ (there exists an edge bet …
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7 votes
2 answers
235 views

Evolution of the empirical mean of a list as we remove elements proportional to their value

Consider a list of $N$ integers $k_1,k_2,\dots k_N$, drawn independently from some distribution $P(k)$ with $k_i \geq 1$. We denote its mean with $\langle k\rangle=\sum_{k=1}kP(k)$. The first two mome …
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  • 274