Title: Shapes and Sizes of Voids in the LCDM Universe: Excursion Set Approach

Abstract: We study the global distribution and morphology of dark matter voids in a LCDM universe using density fields generated by N-body simulations. Voids are defined as isolated regions of the low-density excursion set specified via density thresholds, the density thresholds being quantified by the corresponding filling factors, i.e., the fraction of the total volume in the excursion set. Our work encompasses a systematic investigation of the void volume function, the volume fraction in voids, and the fitting of voids to corresponding ellipsoids and spheres. We emphasize the relevance of the percolation threshold to the void volume statistics of the density field both in the high redshift, Gaussian random field regime, as well as in the present epoch. By using measures such as the Inverse Porosity, we characterize the quality of ellipsoidal fits to voids, finding that such fits are a poor representation of the larger voids that dominate the volume of the void excursion set.