|Speaker :||Mir-Omid Haji-Mirsadeghi|
|Sharif University of Technology|
|Location:||LINCS Seminars room|
In this talk we will define notions of dimension on unimodular random
graphs. The key point in this definition is unimodularity which is used indispensably and distinguishes this view point from the previous notions which are defined in the literature. Other notions which are related to the notion of dimension such as volume growth are discussed which provide a toolset to calculate the dimension. Several examples of such graphs will be discussed in relation with the theory of point processes and that of unimodular graphs. Different methods for finding upper bounds and lower bounds on the dimension will also be presented and illustrated through these examples.