{'fraction_non_alphanumeric': 0.01217391304347826, 'fraction_numerical': 0.0034782608695652175, 'mean_word_length': 5.47191011235955, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Weak Poincaré inequalities for convolution probabilities measures

In this paper, weak Poincaré inequalities are obtained for convolution probabilities with explicit rate functions by constructing suitable Lyapunov functions. Here, one of these Lyapunov functions is introduced for the first time and can be used to improve parts of results on the estimate of rate functions for super Poincaré inequalities 13 as well. In addition, these weak Poincaré inequalities are applied to some concrete examples, which can refine some of results even for the case without convolution.