{'fraction_non_alphanumeric': 0.013232514177693762, 'fraction_numerical': 0.001890359168241966, 'mean_word_length': 5.54320987654321, '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}}
Stochastic Lagrangian flows on some compact manifolds

We investigate ponctual as well as L 2 distances of some stochastic processes with values in the group of homeomorphisms of a compact manifold including processes modelling time evolution of fluids. These processes are associated with operators of the form Laplace–Beltrami plus a first-order term. Several constructions are presented, in particular via coupling methods, the corresponding behaviour of the distance depending on the construction and on the drift properties.