Timeline for Naturally occuring counting process with a 1/log asymptotics?
Current License: CC BY-SA 3.0
5 events
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| Dec 7, 2017 at 13:38 | comment | added | shantanu | The question is where does the 1/log x probability arise from. At the fundamental level a physical system is a realization of a quantum mechanical system defined by a system evolution. There is this notion of reimannian that defines this evolution but that system is only hypothetical and to our knowledge we dont know of a device that implements it. | |
| Dec 6, 2017 at 20:45 | comment | added | Kurisuto Asutora | Another simple counting process having the same density would be any (typical) realization of Cramer's random model of the primes. In this model, for each positive integer x you decide independently with probability 1/log x if it is prime or not. Obviously this gives a sequence with density 1/log. Also, I suppose this is "physically realizable" (by throwing some sort of dice), whatever this term might mean. | |
| Dec 5, 2017 at 21:13 | comment | added | Greg Martin | A program running on a computer is a physical system.... | |
| Dec 4, 2017 at 23:57 | comment | added | shantanu | Thanks for the examples. Would you know if there are physical systems that can implement these different discrete process ? For our device, we are counting the number of electrons so the underlying stochastic process is measuring the total counts \sum_{n \in N} I(n) where I(.) is an indicator function and n is time instant representing the occurrence of an event. | |
| Dec 4, 2017 at 23:19 | history | answered | Greg Martin | CC BY-SA 3.0 |