We survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets.
|Number of pages||15|
|Journal||Trends in Mathematics|
|Early online date||25 Aug 2017|
|Publication status||Published - 2017|