Abstract: Gaussian Boson Sampling is a promising method for experimental demonstrations of quantum advantage. If the probability of getting the same outcome from two independent samples is sufficiently low, one says that the outcome probabilities anticoncentrate, a property that features in arguments for the classical hardness of Gaussian Boson Sampling. In [arXiv:2312.08433, arXiv:2403.13878], we show that Gaussian Boson Sampling undergoes a transition in anticoncentration as a function of the number of modes that are initially squeezed compared to the number of photons measured at the end of the circuit. When the number of initially squeezed modes scales sufficiently slowly with the number of photons, there is a lack of anticoncentration. However, if the number of initially squeezed modes scales quickly enough, the output probabilities anticoncentrate weakly. With the eventual goal of illuminating the relationship between complexity and entanglement, we also study entanglement within the set of modes at the output of Gaussian Boson Sampling when the linear optical unitary is random [arXiv:2209.06838, arXiv:2403.18890].