Correlation btw stock prices and private equity multiples

I'm wondering about the correlation btw stock prices (pe ratio) and the multiples paid for private companies bought by PE. Usually, one would expect that increases in pe ratios would also increase the multiples paid for private companies. However, given the dry powder (demand) I could imagine to maybe have an inverse correlation in the near future (leading to more P2P deals medium term). What's the inside scoop on this? 

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