The Percolation on Cellular Automata

Our aim is to study sensitivity theory and to apply it to a random cellular automata model. We would like to establish when the model is noise-sensitive and connect this property to the limiting behaviour of processes (system of dependent random walks) obtained from the cellular automata model. We would like to establish conditions for its convergence to multidimensional Brownian motions.

Consider the following self-organized system on Z^+×Z^+. The vertices of this lattice are labelled using the familiar Euclidean coordinates. To each vertex we assign a value in {-1,1} according to the following rule. The value at vertex (i,j) is the product of the values at (i, j – 1) and (i -1, j). The system is well defined once we provide the boundary conditions, which are the following. The vertices with coordinates (1, j), with j ≥ 1 have all the same values. The values of the vertices of the form (i, 1), with i ≥ 1 are generated at random according to a certain rule. This project investigates the main features of this system.

Jiayu Li

Monash University

Jiayu is a third-year student from Monash University, studying a Bachelor of Actuarial Science, double major in Mathematical Statistics. During her study, she finds the topic on probability theory and stochastic processes very enlightening and interesting! She is passionate about theoretical research and applications of stochastic processes in finance and sciences. Jiayu is also interested in mathematics education and she loves attending the talks and seminars around this topic. Outside mathematics, she enjoys music and various styles of dances.

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