Compressive　sensing　(CS)　provides　a　new　paradigm　for　efficient　data　gathering　in　wireless　sensor　networks　(WSNs).　In　this　paper,　with　the　assumption　that　sensor　data　is　sparse　we　apply　the　theory　of　CS　to　data　gathering　for　a　WSN　where　n　nodes　are　randomly　deployed.　We　investigate　the　fundamental　limitation　of　data　gathering　with　CS　for　both　single-sink　and　multi-sink　random　networks　under　protocol　interference　model,　in　terms　of　capacity　and　delay.　For　the　single-sink　case,　we　present　a　simple　scheme　for　data　gathering　with　CS　and　derive　the　bounds　of　the　data　gathering　capacity.　We　show　that　the　proposed　scheme　can　achieve　the　capacity　Theta(nW/M)　and　the　delay　Theta(M　root　n/log　n),　where　W　is　the　data　rate　on　each　link　and　M　is　the　number　of　random　projections　required　for　reconstructing　a　snapshot.　The　results　show　that　the　proposed　scheme　can　achieve　a　capacity　gain　of　Theta(n/M)　over　the　baseline　transmission　scheme　and　the　delay　can　also　be　reduced　by　a　factor　of　Theta(root　n　log　n/M).　For　the　multi-sink　case,　we　consider　the　scenario　where　n(d)　sinks　are　present　in　the　network　and　each　sink　collects　one　random　projection　from　n(s)　randomly　selected　source　nodes.　We　construct　a　simple　architecture　for　multi-session　data　gathering　with　CS.　We　show　that　the　per-session　capacity　of　data　gathering　with　CS　is　Theta(n　root　nW/Mn-d　root　n(s)　log　n)　and　the　per-session　delay　is　Theta(M　root　n/log　n).　Finally,　we　validate　our　theoretical　results　for　the　scaling　laws　of　the　capacity　in　both　single-sink　and　multi-sink　networks　through　simulations.