This is a difficult question.  I cannot find any research on the matter. Growers suggest that horseradish is somewhat sensitive to juglone but that it can be grown in raised beds outside the dripline of the walnut.  The dripline is a line extending straight down from the widest point of the tree canopy to the ground--as if the tree were an umbrella.
I am sorry to not pass on scientific studies to you.  I can not find any.  

Thanks so much!
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