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Department of Mathematics, Applied Mathematics and Statistics

Department of Mathematics, Applied Mathematics and Statistics

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Home / Abstracts / Undergraduate Colloquium- April 11, 2014

Undergraduate Colloquium- April 11, 2014

Posted on April 11, 2014

Friday, April 11, 2014 (4:00 – 5:00 p.m. in Yost 306)

Title: A Model for Gang Territoriality Motivated By Graffiti

Speaker: Alethea Barbaro (Case Western Reserve University)

Abstract: In cities with a lot of gang activity, police and residents can often map out every gang’s territory, down to the block and sometimes even down to which side of a street belongs to which gang.  One activity of the younger members of a gang is to advertise the gang by “tagging”, and there is evidence that this may be one of the ways that a gang claims territory.  In this talk, we discuss a model for territorial formation which is motivated by gang graffiti. We begin with a particle model on a lattice with agents belonging to two gangs.  These agents then put down graffiti and move preferentially away from sites marked by the other gang. For certain parameters, the agents gradually segregate into distinct territories.  We reframe the model as a spin model with a Hamiltonian which captures the same basic dynamics and prove that a phase transition occurs in two dimensions.