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"From what I have heard and read so far the stories are of concern to myself, my wife and also my children as they have seen reports on 'You Tube'," Walton said in a statement.
"As a result, we felt the best thing at this point was to write to An Taoiseach (the prime minister) ourselves to get more details and the exact context of the various stories."
The statement said Walton, who holed the winning putt in the 1995 Ryder Cup, felt "anger" at this week's events.
Walton is said to have conquered a stutter in his youth and is awaiting a reply from Offaly Brian.
