Consumption of walnuts is associated with a reduction in all-cause mortality.

Study: Frequency of nut consumption and mortality risk in the PREDIMED nutrition intervention trial

People who ate walnuts regularly were much less likely to die from any cause during the study, even after accounting for other health factors. The more walnuts they ate, the lower their risk of death.

Study: Association of Walnut Consumption with Total and Cause-Specific Mortality and Life Expectancy in U.S. Adults

People who ate walnuts five or more times a week lived longer on average than those who never ate them — about 1.3 years longer. The more walnuts people ate, the less likely they were to die from any cause.

Study: Walnut Consumption Alters the Gastrointestinal Microbiota, Microbially Derived Secondary Bile Acids, and Health Markers in Healthy Adults: A Randomized Controlled Trial

Eating walnuts every day improved gut bacteria and lowered 'bad' cholesterol in this study, which are things linked to living longer. So it suggests walnuts might help people live longer, even though the study didn’t track deaths directly.

Study: Diet, cardiovascular disease, and mortality in 80 countries

People who ate more nuts, including walnuts, along with fruits and vegetables, were 30% less likely to die from any cause during the study. So eating walnuts as part of a healthy diet is linked to living longer.