Thema der Dissertation:
Coarse Graining of Agent-Based Models and Spatio-Temporal Modeling of Spreading Processes Thema der Disputation:
Card Shuffling, Magic and True Randomness
Coarse Graining of Agent-Based Models and Spatio-Temporal Modeling of Spreading Processes Thema der Disputation:
Card Shuffling, Magic and True Randomness
Abstract: Card tricks are an essential part of magic performances, and a classic variation is to find a card chosen by the audience in a seemingly random deck of cards. While many tricks are based on creating the illusion of interacting with the deck or skilled sleight of hand, some performers also use mathematical properties of card shuffling. Perfect shuffles can restore order to a chaotic arrangement, and residual structures after shuffling a previously ordered deck can be used to identify a selected card. This raises the question of whether human shuffling can properly randomize a deck of cards, and if so, how many shuffles are required?
In this talk, we will explore some famous results on the mathematics of card shuffling based on the analysis of the Gilbert-Shannon-Reeds (GSR) model for riffle shuffles. We will discuss the patterns that emerge from repeated riffle shuffles and the convergence to uniform random permutations. Finally, we will take a brief look at some numerical experiments based on Monte Carlo sampling to analyze a geometric model of (biased) riffle shuffles that may be closer to actual human card shuffling than the GSR model.
In this talk, we will explore some famous results on the mathematics of card shuffling based on the analysis of the Gilbert-Shannon-Reeds (GSR) model for riffle shuffles. We will discuss the patterns that emerge from repeated riffle shuffles and the convergence to uniform random permutations. Finally, we will take a brief look at some numerical experiments based on Monte Carlo sampling to analyze a geometric model of (biased) riffle shuffles that may be closer to actual human card shuffling than the GSR model.
Zeit & Ort
09.11.2023 | 14:00
Seminarraum
(Zuse Institut Berlin, Takustr. 7, 14195 Berlin)