From: Martin Nowak To: Jeffrey Epstein <jeevacation@gmail.com> Subject: Fwd: Re: Date: Sun, 02 Jan 2011 22:55:05 +0000 Attachments: Coming_together_vl.pdf ... from Clifford henry taubes Begin forwarded message: From: Clifford Tauber • Date: January 2, 2011 4:57:11 PM EST To: Martin Nowak Cc: Corina Tamita Subject: Re: Hi Martin and Corina, I have attached a pdf with what I think at this hour is the correctly stated proposition about existence/uniqueness. The proof is given. You will notice that the various inequalities, statements, etc are completely different (going in the other direction even!) from what I said in earlier emails. This is due to me making my canonical error and reversing a crucial inequality. Corina: Can you check the argument VERY CLOSELY as my probability for making a sophomoric mistake in any given step is closing in on 55%; and as there are a number of steps, the total probability for having screwed up is likely greater than 90%. Best wishes, Cliff On Jan I, 2011, at 10:03 PM, Martin Nowak wrote: cliff, corina in the (few) simulations that i have done for CT phi i have never seen multiple stable interior equilibria. so in this (very weak) sense my simulations certainly EFTA00901691 do not disprove cliff's conjecture. but could you construct a case where you expect multiple stable interior equilibria to exist. i would love to study such a case. EFTA00901692