Linear-size autocatalytic sets are asymptotically absent in the sparse binary polymer model
In the sparse binary-polymer model with reversible ligation and cleavage, fix the food-length bound t, a nonnegative catalysis intensity lambda, and a linear reaction budget Cn. As the maximum polymer length n tends to infinity, the probability of a nonempty reflexively autocatalytic and food-generated reaction set with at most Cn channels tends to zero. The probability that some molecule catalyses a nonempty food-generated reaction set that constructs that molecule also tends to zero. These statements address the linear-size and single-molecule self-construction questions for the sparse…
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