We will give an alternative proof of the theorem by D. Witte, stating that an amenable left orderable group is locally indicable, i.e. every finitely generated subgroup has a non trivial morphism to the integers. We will then explain some properties of symmetric random walks on left orderable groups, and related problems. This latter part is a joint work with V. Kleptsyn, A. Navas and K. Parwani.