We consider the spatially inhomogeneous Moran model with seed-banks introduced in den Hollander and Nandan (2021). Populations comprising active and dormant individuals are structured in colonies... Show moreWe consider the spatially inhomogeneous Moran model with seed-banks introduced in den Hollander and Nandan (2021). Populations comprising active and dormant individuals are structured in colonies labelled by Zd, d≥1. The population sizes are drawn from an ergodic, translation-invariant, uniformly elliptic field that form a random environment. Individuals carry one of two types: ♡, ♠. Dormant individual resides in what is called a seed-bank. Active individuals exchange type from seed-bank of their own colony and resample type by choosing parent from the active populations according to a symmetric migration kernel. In den Hollander and Nandan (2021) by using a dual (an interacting coalescing particle system), we showed that the spatial system exhibits a dichotomy between clustering (mono-type equilibrium) and coexistence (multi-type equilibrium). In this paper we identify the domain of attraction for each mono-type equilibrium in the clustering regime for a fixed environment. We also show that when the migration kernel is recurrent, for a.e. realization of the environment, the system with an initially consistent type distribution converges weakly to a mono-type equilibrium in which the fixation probability to type-♡ configuration does not depend on the environment. A formula for the fixation probability is given in terms of an annealed average of type-♡ densities in dormant and active population biased by ratio of the two population sizes at the target colony.Primary techniques employed in the proofs include stochastic duality and the environment process viewed from particle, introduced in Dolgopyat and Goldsheid (2019) for random walk in random environment on a strip. A spectral analysis of Markov operator yields quenched weak convergence of the environment process associated with the single-particle dual process to a reversible ergodic distribution, which we transfer to the spatial system of populations by using duality. Show less
Este artículo examina la filosofía de la vida de Nietzsche. Para ello se enmarca 1) dentro de la ontología Nietzscheana del conflicto y la lucha en tanto que dimensión irreducible de la existencia... Show moreEste artículo examina la filosofía de la vida de Nietzsche. Para ello se enmarca 1) dentro de la ontología Nietzscheana del conflicto y la lucha en tanto que dimensión irreducible de la existencia humana a todos los niveles y 2) dentro del intento por parte de las ‘teorías agonísticas’ de incorporar este supuesto a la teoría democrática. Para comenzar, en oposición a la metafísica tradicional (i.e. a la ontología de la sustancia), la filosofía nietzscheana de la vida se presenta como una ontología dinámica y relacional del conflicto entre poderes que no están sujetos a ninguna sustancia. Partiendo de este concepto de vida surge la pregunta: ¿cuáles son las implicaciones políticas del compromiso nietzscheano con la afirmación y con el realce o intensificación (Steigerung) de la vida? En contraposición a la interpretación común, según la cual Nietzsche abogaría por la dominación y la violencia, este texto sostiene que, según Nietzsche, la vida es intensificada al máximo cuando la lucha (o tensión) y la pluralidad son maximizadas; y que esa lucha y pluralidad son maximizadas sólo en el caso de que haya un equilibrio aproximado entre fuerzas más o menos iguales, y no bajo condiciones de dominación. Aplicando esta línea de pensamiento a la cuestión de la naturaleza y al estatus de la ley resulta que la filosofía de la vida de Nietzsche aboca en una afirmación de pluralidad de órdenes legales en tensión constructiva, lo que nos invita a plantear la pregunta acerca de las condiciones institucionales que harían esto posible. Palabras claves: conflicto - agón - ontología de la sustancia - equilibrio -ley. ABSTRACT: This paper examines Nietzsche’s philosophy of life against the background claim that conflict and struggle constitute an irreducible dimension of human existence at all levels and the attempt on the part of ‘agonistic theorists’ to incorporate this claim into democratic theory. To begin with, Nietzsche’s philosophy of life is set out against traditional metaphysics (substance ontology) as a dynamic, relational ontology of conflict among powers without substance. Given this concept of life, what, then, are the political implications of Nietzsche commitment to life-affirmation and life-enhancement? Against the standard view that Nietzsche advocates domination and violence, it is argued that life is maximally enhanced when struggle(or tension) and plurality are maximised, and that struggle and plurality are maximised under conditions of an approximate equilibrium among more or less equal forces, and not under conditions of domination. This line of thought is applied to the question of the nature and status of law with the result that Nietzsche’s philosophy of life issues in an affirmation of a plurality of legal orders in constructive tension with one another, raising the question of the institutional conditions that would make this possible Show less
