Many genes have divergent transcripts in the antisense orientation. These divergent transcripts are quickly degraded. Double peaks at TSSs represent it's association with the gene and it's cognate RNA (divergent transcript). The dip between these two peaks represent nucleosome free region.
To understand more on your answer. Are you trying to say that the region between the peaks, which is where there is a reduced H3k4me3, is a nucleosome free region ? Are you suggesting that most of the TSS regions associated with the H3K4me3 are nucleosome free ?
Please elaborate on this.