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We study the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. By a coupling approach, we establish global contraction in an $L^1$ Wasserstein distance with an explicit dimension-free rate for pairwise weak interactions. For external forces corresponding to a $\kappa$-strongly convex potential, a contraction rate of order $\mathcal{O}(\sqrt{\kappa})$ is obtained in certain cases. But the contraction result is not restricted to these forces. It rather includes multi-well potentials and non-gradient-type external forces as well as non-gradient-type repulsive and attractive interaction forces. The proof is based on a novel distance function which combines two contraction results for large and small distances and uses a coupling approach adjusted to the distance. By applying a componentwise adaptation of the coupling we provide uniform in time propagation of chaos bounds for the corresponding mean-field particle system., Comment: 34 pages, 2 figures

We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for the corresponding mean-field particle system approximations. Our approach is based on a sticky coupling between two solutions to the equation. We show that the distance process between the two copies is dominated by a solution to a one-dimensional nonlinear stochastic differential equation with a sticky boundary at zero. This new class of equations is then analyzed carefully. In particular, we show that the dominating equation has a phase transition. In the regime where the Dirac measure at zero is the only invariant probability measure, we prove exponential convergence to equilibrium both for the one-dimensional equation, and for the original nonlinear SDE. Similarly, propagation of chaos is shown by a componentwise sticky coupling and comparison with a system of one dimensional nonlinear SDEs with sticky boundaries at zero. The approach applies to equations without confinement potential and to interaction terms that are not of gradient type., Comment: 46 pages

Die vorliegende Masterarbeit beschäftigt sich mit der Darstellung von jüdisch-amerikanischen Protagonisten aus zweiter und dritter Generation und deren Identitätskrise in Kurzgeschichten aus den 1950er Jahren. Für die Analyse werden die Kurzgeschichtensammlungen The Magic Barrel (1958) von Bernard Malamud und Goodbye, Columbus and Five Short Stories (1959) von Philip Roth herangezogen. Der theoretische Hintergrund dieser Masterarbeit setzt sich aus den Bereichen der Judaistik sowie der Männerforschung zusammen. Die Analyse orientiert sich an den Konzepten des Jüdischen Selbsthasses, dem Moralkodex der Menschlichkeit und einem beziehungsorientierten Zugang zu verschiedenen Arten von Männlichkeit. Die Literaturanalyse zeigt, dass die Protagonisten von der amerikanischen Mittelschicht trotz erfolgreicher Assimilation an die Grenze der Gesellschaft gedrängt werden. Sie eifern dem unerreichbaren Ideal von amerikanischer Männlichkeit hinterher und werden von Gefühlen der Unzulänglichkeit geplagt, welche von den Frauen in ihrem Leben noch weiter verstärkt werden. Die Identitätskrisen werden durch Begegnungen mit anderen jüdischen Charakteren ausgelöst und bringen die männlichen Protagonisten dazu, den Stellenwert ihrer jüdischen Herkunft zu überdenken und ihre amerikanische Sozialisation in Frage zu stellen. Ihre Identitätskrisen sind oft von Selbsthass geprägt, welcher durch ein Bekenntnis zur Jüdischen Gemeinschaft überwunden werden können. Die Protagonisten lernen Verantwortung für ihre jüdischen Mitmenschen zu übernehmen und sind somit nicht mehr nur Männer, sondern auch wahre Menschen im Sinne der jüdischen Morallehre. Letzen Endes sind sie dazu in der Lage, die Vielschichtigkeit ihrer männlichen, und sowohl amerikanischen also auch jüdischen, Identität zu akzeptieren., This Master’s thesis examines the identity crises experienced by second or third generation Jewish American male characters in selected short stories from Bernard Malamud’s short story collection The Magic Barrel (1958) and Philip Roth’s short story collection Goodbye, Columbus and Five Short Stories (1959). The theoretical background of this thesis includes concepts from the fields of Jewish studies and masculinity studies. Jewish self-hatred, the moral code of menshlichkeit and a relational approach to the construction of masculinities are guiding the analysis. A close reading of the authors’ short fiction showed that their stories depict middle-class lives that are divided along ethnic and religious lines and the marginalization of Jewish American men is visible through the absence of ties to gentile, white America. At the core of several of the protagonists’ struggles lies a crisis revolving around their Jewish identity, which is inextricably linked to their perception of masculinity. They strive towards the unreachable ideal of hegemonic American masculinity in the face of their own inadequacy. The protagonists’ insecurities are reinforced by their relationship with women. The female characters in these short stories are not only used to further the men’s personal and spiritual development, but they also have the power to emasculate them. Moreover, all of the protagonists’ crises are triggered by fateful encounters with other Jewish characters that make them reconsider the significance of their own Jewishness in their lives and the quality of American middle-class values. The characters’ feelings of self-hatred are often overcome by recognizing their part in the Jewish community and taking responsibility for other members, which is indicative of the moral code of menshlichkeit. Therefore, the question of “Man or Mensch?” needs to be replaced by the statement “Man and Mensch”, which exemplifies the male characters’ multi-layered masculine and national identities.