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Consider a large $N\times N$ square lattice, where each cell has a probability $p$ of being "occupied" (let's call denote them as "black") and a probability $1-p$ of being empty (let's denote them as "...

Consider a matrix whose elements are independently assigned a value $1$ with probability $p$ and a value $0$ with probability $1-p$. Define a cluster of cells as a maximal connected component in the ...

This is a sequel to the question: Why is number of single cell clusters always greatest in a random matrix? In their answer, @Aaron Meyerowitz came up with a nice strategy to prove why the number of ...

Context: This a sequel to the question: Is the Erdős–Rényi giant component result applicable here? Consider a matrix whose elements are independently assigned a value $1$ with probability $p$ ...