We present a deep I,Z photometric survey covering a total area of 1.12 deg^{2} of the Sigma Orionis cluster (Icompl=22 and Zcompl=21.5mag). From I, I-Z color-magnitude diagrams we have selected 153 candidates that fit the previously known sequence of the cluster. Using J-band photometry, we find that 124 of the 151 candidates follow the previously known infrared photometric sequence of the cluster and are probably members. We have studied the spatial distribution of these candidates and found that there are objects located at distances greater than 30 arcmin to the north and west of Sigma Orionis that probably belong to different populations of the Orions Belt. For the 102 bona fide Sigma Orionis cluster member candidates, we find that the radial surface density can be represented by a decreasing exponential function (sigma = sigma_0 e^{-r/r_0}) with a central density of sigma_0=0.23+/-0.03 object/arcmin^{2} and a characteristic radius of r_0=9.5+/-0.7 arcmin. From a statistical comparison with Monte Carlo simulations, we conclude that the spatial distribution of the cluster member candidates is compatible with a Poissonian distribution and, hence, they are not mainly forming aggregations or sub-clustering. Using near-infrared JHK-band data from 2MASS and UKIDSS and mid-infrared data from IRAC/Spitzer, we find that 5-9 % of the brown dwarf candidates in the Sigma Orionis cluster have K-band excesses and 31+/-7 % of them show mid-infrared excesses at wavelengths longer than 5.8 microns, which are probably related to the presence of disks. We have also calculated the initial mass spectrum (dN/dm) of Sigma Orionis from very low mass stars (0.10 Msol) to the deuterium-burning mass limit (0.012-0.013 Msol). This is a rising function toward lower masses and can be represented by a power-law distribution (dN/dm = m^{-alpha}) with an exponent alpha of 0.7+/-0.3 for an age of 3 Myr.
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