and at the i start randomly so at the beginning it's zero and then it is growing event or not but here it is growing and depending on the value of the noise so there's the delta p here so darker line here is larger delta p so larger noise is harder and indeed you are seeing that when it goes up the value at which it saturates is lower for the larger noise so that's intuitive should be lower correlation because it's higher noise so it's a harder problem but what's not intuitive is that it actually for larger noise the correlation the