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Anderson, 52, and Peters, 74, got married in Malibu on January 20 in a private ceremony but never filed for a marriage certificate.
“I have been moved by the warm reception to Jon and my union. We would be very grateful for your support as we take some time apart to re-evaluate what we want from life and from one another,” Anderson said in a statement to The Hollywood Reporter.
“Life is a journey and love is a process. With that universal truth in mind, we have mutually decided to put off the formalization of our marriage certificate and put our faith in the process. Thank you for respecting our privacy,” she added.
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Anderson was previously married to rocker Tommy Lee, Kid Rock, and Rick Solomon. She was recently linked to the French soccer icon Adil Rami.