The 'fat' bars are only fat at the stem clamp area- that's where you need to be sure to match the stem's clamp size with the bar's diameter at the clamp area.
The grip area, as well as the area for mounting shifters and levers, is standardized. You'll find that shifters and levers are made to fit this standard- which, if I recall correctly, is 7/8 inch.
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"I tell you, We are here on earth to fart around, and don't let anybody tell you any different." - Kurt Vonnegut jr.