Hippocampal place cells have single, bell-shaped place fields in small environments. Recent experiments, however, reveal that, in large environments, place cells have multiple fields with heterogeneous shapes and sizes. We show that this diversity is explained by a surprisingly simple mathematical model, in which place fields are generated by thresholding a realization of a random Gaussian process. The model captures the statistics of field arrangements and generates new quantitative predictions about the statistics of field shapes and topologies. These predictions are quantitatively verified in bats and rodents, in one, two, and three dimensions, in both small and large environments. These results imply that common mechanisms underlie the diverse statistics observed in different experiments and further suggest that synaptic projections to CA1 are predominantly random.

Keywords: CA1; computational neuroscience; hippocampus; neural coding; place cells; spatial cognition; theoretical neuroscience.

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