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Some mathematics research can, at first glance, look a lot like child's play. Here, for instance, is the question that's been occupying research student Ori Gurel Gurevich in the group of Prof. Itai Benjamini of the Weizmann Institute's Mathematics Department: Can patterns arise from a random distribution? For example, if an infinite floor is laid with black and white tiles, each chosen randomly, will there be, nonetheless, some kind of order? If the black tiles can be thought of as "dry land" to the white tile's "water," what are the chances that, instead of scattered islands, they'll form a sizable continent?
"My first mathematical memory is of a television program on whole numbers and fractions. The program hinted at the existence of irrational numbers, and that fired my imagination."
The answer lies in probability. If white tiles outnumber the black ones by quite a bit (mathematically speaking – a low probability of choosing black), the black areas will remain islands, but if the probability is high, a continent will form as well. Is there a distinct borderline between these two states of existence? From this research, it's become clear that different types of tiles cross from one "state" to another at different thresholds. For instance, if the tiles are hexagonal, a continent starts to form when the odds of picking one or the other are equal. On the other hand, the transition states for all tiles share a number of features that are not dependent on the tile shape.
Such theoretical studies can have a number of very practical applications, shedding light, for instance, on phase transitions – the change from one state to another – in materials science.
"The Weizmann Institute Graduate School allows me to focus on pure research with no interruptions."
Ori Gurel Gurevich’s research in the lab of Prof. Itai Benjamini is supported by the Arthur and Rochelle Belfer Institute of Mathematics and Computer Science.