Random arrays of single molecules are provided for carrying out large scale analyzes, particularly of biomolecules, such as genomic DNA, cDNAs, proteins, and the like. In one aspect, arrays of the invention comprise concatemers of DNA fragments that are randomly disposed on a regular array of discrete spaced apart regions, such that substantially all such regions contain no more than a single concatemer. Preferably, such regions have areas substantially less than 1 μm2 and have nearest neighbor distances that permit optical resolution of on the order of 109 single molecules per cm2. Many analytical chemistries can be applied to random arrays of the invention, including sequencing by hybridization chemistries, sequencing by synthesis chemistries, SNP detection chemistries, and the like, to greatly expand the scale and potential applications of such techniques.