Explanation of probability of forks in the Bitcoin blockchain I am reading this paper on how information is propagated on the Bitcoin network. The authors present a model to predict the rate at which forks occur in the blockchain which is given as below

Here, F is the number of conflicting blocks in the network, Pb is the probability of the network finding a block b in a given second (ideally, 1/600 since a block is expected every 10 mins = 600 secs) and f(t) represents the ratio of nodes that hear about the block b in t secs. However, what I cannot understand is how this entire expression is derived. I understand that the term in the exponent represents the mean amount of time it takes for the network to learn about a block (and this value can be derived from a graph given in the paper). I assume 1 - Pb represents the probability of the network finding more blocks in the remaining 599 seconds in the 10-minute interval. Why is this probability raised to the mean amount of time it takes for the network to learn about a block?

Any explanation would be appreciated.
I haven't read the paper, and I think the expression is only an approximation, but the basic idea is that this is an inhomogeneous Poisson process.

In order for a fork to occur, some unaware node needs to find a block. This is 1 minus the probability that no unaware node will ever find a block. Which itself means that no unaware node finds a block in 1st second, no unaware node find a block in 2nd second, etc. This probability is the product of the probabilities of the individual seconds (since they are all independent).

Each individual probability is roughly (1-P_b)^(1-f(t)) (if f(t)=0 then all nodes are unaware and the probability is the same as no block being found at all a block at all, if f(t)=1 then all nodes are aware and certainly no block will be found by an unaware node, and in between it interpolates. If it's not clear why the interpolation is via a power, keep in mind that for small P_b, the power is irrelevant since the expression is roughly 1-P_b*(1-f(t)).

The combined probability, as mentioned, is the product of probabilities, which is like (1-P_b) to the power of a sum of (1-f(t)), which is like (1-P_b) to the power of an integral.

If it was up to me I would have written the expression differently, but these are the general ideas.