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Even as states across the country have legalized marijuana, potentially opening the door to a multibillion dollar industry, the impact of marijuana criminalization is still being felt by people — mostly black and Hispanic — whose records are marked by low-level convictions related to the drug.

But on Wednesday, New York began the process of expunging many of those records, as part of a new state law to reduce penalties associated with marijuana-related crimes, a spokesman for Gov. Andrew M. Cuomo confirmed.

“For too long communities of color have been disproportionately impacted by laws governing marijuana and have suffered the lifelong consequences of an unfair marijuana conviction,” Mr. Cuomo said in a statement.

Under the new law, which was passed in June and took effect on Wednesday, about 160,000 people with marijuana convictions in the state will have those convictions cleared from their record, according to a spokeswoman for the State Division of Criminal Justice Services .