Clement Canonne Distributed Simulation and Distributed Inference: Algorithms, Tradeoffs, and a Conjecture Independent samples from an unknown probability distribution p on a domain of size k are distributed across n players, with each player holding one sample. Each player can communicate L bits to a central referee in a simultaneous message passing (SMP) model of communication, with the goal of resolving a prespecified inference problem. When L >= log k bits, the problem reduces to the well-studied centralized case, where all the samples are available in one place. In this work, we focus on the communication-starved setting L < log k, in which the landscape may change drastically. We propose a general formulation for inference problems in this distributed setting, and instantiate it to two prototypical inference questions, learning and uniformity testing. Joint work with Jayadev Acharya (Cornell University) and Himanshu Tyagi (IISc Bangalore).