Tags » Random Walk

Forkable Strings are Rare

In a blockchain protocol such as Bitcoin, the users see the world as a sequence of states. A simple yet functional view of this world, for the purpose of analysis, is a Boolean string of zeros and ones, where each bit is independently biased towards favoring the “bad guys.” 1,702 more words

Mathematics

Some Facts about the Gambler's Ruin Problem

Consider a random walk in the two-dimensional discrete space, where the horizontal direction is indexed by nonnegative time steps and the vertical direction is indexed by integers. 194 more words

Mathematics

splitting a field by annealing

A recent riddle that I pondered about during a drive to Luxembourg last weekend was about splitting a square field into three lots of identical surface for a minimal length of separating wire… While this led me to conclude that the best solution was a T like separation, I ran a simulated annealing R code on my train trip to… 276 more words

Statistics

Gist 1 - Random Walking 1

The following window contains a GitHub gist that I created, which explains some Python basics and plays a little bit with a random walker. The fun thing about gists is, of course, that you can use them interactively, but unfortunately you cannot do that through WordPress (at least I don’t know how to do that, if possible). 58 more words

Basic Plots

Monte Carlo calculations of the radial distribution functions for a proton-electron plasma

“In conclusion, the Monte Carlo method of calculating radial distribution functions in a plasma is a feasible approach if significant computing time is available (…) The results indicate that at least 10000 iterations must be completed before the system can be considered near to its equilibrium state, and for a badly chosen starting configuration, the run would need to be considerably longer (…) for more conclusive results a longer run is needed so that the energy of the system can settle into an equilibrium pattern and steady-state radial distribution functions can be obtained.” A.A.

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Le Monde puzzle [#1024]

The penultimate and appropriately somewhat Monty Hallesque Le Monde mathematical puzzle of the competition!

A dresser with 5×5 drawers contains a single object in one of the 25 drawers.

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Books