We analyze the clustering of galaxies in the first public data release of the Hyper Suprime-Cam Subaru Strategic Program. Despite the relatively small footprints of the observed fields, the data are an excellent proxy for the very deep photometric datasets that will be acquired by the Large Synoptic Survey Telescope, and are therefore an ideal test bed for the analysis methods being implemented by the LSST Dark Energy Science Collaboration. We select a magnitude limited sample with i < 24.5 and analyze it in four tomographic redshift bins covering the range 0.15 z 1.5. We carry out a Fourier-space analysis of the two-point clustering of this sample, including all auto-and cross-correlations between bins. We demonstrate the use of map-level deprojection methods to account for non-physical fluctuations in the galaxy number density caused by observational systematics. Through a halo occupation distribution analysis, we place constraints on the characteristic halo masses of this sample as a function of redshift, finding a good fit up to scales k max = 1 Mpc −1 , including both auto-and cross-correlations. Our results show monotonically decreasing average halo masses with increasing redshift, which can be interpreted in terms of the drop-out of red galaxies at high redshifts for a flux-limited sample, consistent with previous analyses. In terms of photometric redshift systematics, we show that additional care is needed in order to marginalize over uncertainties in the redshift distribution in galaxy clustering, even for samples of this small size, and that these uncertainties can be significantly constrained by including cross-bin correlations. We are able to make a ∼ 3σ detection of the effects of lensing magnification in the HSC data. Our results are stable to variations in the amplitude of density fluctuations σ 8 and the cold dark matter abundance Ω c and we find constraints that agree well with measurements from Planck and low-redshift probes. Finally, we use our analysis pipeline to study the clustering of galaxies as a function of limiting flux, and provide a simple fitting function for the linear galaxy bias for magnitude limited samples as a function of limiting magnitude and redshift. Discussion and Conclusions 50A Reconstructing depth from discrete sources 54

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We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin equation fulfill the appropriate fluctuation-dissipation relation, the probability density on a finite interval converges for long times towards the expected uniform distribution prescribed by thermal equilibrium. In contrast, on a semi-infinite interval with a reflecting wall at the origin, the probability density shows pronounced deviations from the Gaussian behavior observed for normal diffusion. If the correlations of the random force are persistent (positive), particles accumulate at the reflecting wall while anti-persistent (negative) correlations lead to a depletion of particles near the wall. We compare and contrast these results with the strong accumulation and depletion effects recently observed for non-thermal fractional Brownian motion with reflecting walls, and we discuss broader implications. arXiv:1907.08188v1 [cond-mat.stat-mech]