I would like to know if there is a way to express or approach the probability to find a random word w (size lw) in a random text t (size lt), using approximate search tools like tre-agrep with a maximum Levenshtein distance of n. Let's say the size of my alphabet a is la.
For small lw and lt, i can get an approximation with a simple and violent algorithm taking a random word w, generating every possible texts of length lt and counting the number of texts where w is found with a distance of n or less.
With la=4 and lt=20, i already have more than 1E12 possible texts.
Does anyone know if some work has already be done about this question or anything close enough to be useful ?