In this paper, we study random gossip processes in communication models that describe the peer-to-peer networking functionality included in standard smartphone operating systems. Random gossip processes spread information through the basic mechanism of randomly selecting neighbors for connections. These processes are well-understood in standard peer-to-peer network models, but little is known about their behavior in models that abstract the smartphone peer-to-peer setting. With this in mind, we begin by studying a simple random gossip process in the synchronous mobile telephone model (the most common abstraction used to study smartphone peer-to-peer systems). By introducing a new analysis technique, we prove that this simple process is actually more efficient than the best-known gossip algorithm in the mobile telephone model, which required complicated coordination among the nodes in the network. We then introduce a novel variation of the mobile telephone model that removes the synchronized round assumption, shrinking the gap between theory and practice. We prove that simple random gossip processes still converge in this setting and that information spreading still improves along with graph connectivity. This new model and the tools we introduce provide a solid foundation for the further theoretical analysis of algorithms meant to be deployed on real smartphone peer-to-peer networks. More generally, our results in this paper imply that simple random information spreading processes should be expected to perform well in this emerging new peer-to-peer setting.