Large deviations and slowdown asymptotics for one-dimensional excited random walks

We study the large deviations of one-dimensional excited random walks. We prove a large deviation principle for both the hitting times and the position of the random walk and give a qualitative description of the respective rate functions. When the excited random walk is transient with positive speed $v_0$, then the large deviation rate function for the position of the excited random walk is zero on the interval $[0,v_0]$ and so probabilities such as $P(X_n < nv)$ for $v \in (0,v_0)$ decay subexponentially. We show that rate of decay for such slowdown probabilities is polynomial of the order $n^{1-\delta/2}$, where $\delta>2$ is the expected total drift per site of the cookie environment.Comment: 23 pages, 3 figure

Is Coming into Existence Always a Harm? Qoheleth in Dialogue with David Benatar

Contemporary philosopher David Benatar has advanced the self-evidently controversial claim that “coming into existence is always a harm.” Benatar’s argument turns on the basic asymmetry between pleasure and pain, an asymmetry he seeks to explain by the principle that those who never exist cannot be deprived. Benatar’s import is almost incredible: humans should cease to procreate immediately, thereby engendering the extinction of the species—a view known as “anti-natalism.” According to many of his readers, the ancient Hebrew sage Qoheleth expresses a pessimistic nihilism that runs as thick as Benatar’s. Prima facie grounding for this assertion is that Qoheleth, like Benatar, raises the issue of whether coming into existence may be a harm—and gives an affirmative answer. In two passages, Ecclesiastes 6:1-6 and 4:1-3, Qoheleth declares that an unborn hypothetical person is “better off” than their existent counterpart. Yet the meaning and implication of these words is far from obvious. Does Qoheleth imply that the non-exister’s state, and non-existence in general, is universally superior to existence? Or is he instead speaking exceptionally, of particular persons in rare circumstances? By examining the two “better”-statements in their literary context, I will argue that Qoheleth intends these examples as exceptions. He does not go so far as to make the supremely nihilistic claim that coming into existence is always, or even generally, a net harm; yet, he does concede that in certain cases, it can be. Beyond this, I will explore how the two thinkers’ divergent conclusions can be traced to a deeper difference of philosophical method. This question concerning non-existence opens a window to Qoheleth’s broader scheme of values and therefore serves as a surprisingly useful entry point by which to engage his philosophy. The paper utilizes the methodology Jaco Gericke has recently termed “philosophical criticism,” but specifically applied to Qoheleth

Living with difference in hyper-diverse areas: how important are encounters in semi-public spaces?

Urban populations increasingly diversify in their socio-economic, cultural, religious and linguistic profiles as well as in their lifestyles, attitudes and activity patterns. This hyper-diversification can complicate feelings of belonging and community. Since diversity is negotiated at the neighbourhood level, micro spaces are central in building communities. Micro spaces tend to be semi-public and stimulate diverse groups to intermingle, which results in on–off as well as repetitive and structural interactions. Understanding the creation and impact of encounters is central to capturing contemporary notions of belonging and living with difference. This paper compares encounters experienced in two semi-public spaces in the hyper-diverse neighbourhood of Feyenoord in Rotterdam, the Netherlands. Although encounters at the library were lighter and shorter than at the community-centre, all positively impact collective life in the neighbourhood. At the community-centre, encounters result in light as well as deeper relationships, making visitors feel more at ‘home’ because they recognize others elsewhere in the neighbourhood. At the library, encounters are lighter but visitors become familiar with diversity, making them feel more at ‘home’ and safe in their neighbourhood as well. The study suggests that fleeting encounters require more serious attention within the context of negotiating diversity

The Classroom

Postcard from Sara Peterson, during the Linfield College Semester Abroad Program at Telemark University in Bø, Norwa

Large deviations for random walks in a random environment on a strip

We consider a random walk in a random environment (RWRE) on the strip of finite width $\mathbb{Z} \times \{1,2,\ldots,d\}$. We prove both quenched and averaged large deviation principles for the position and the hitting times of the RWRE. Moreover, we prove a variational formula that relates the quenched and averaged rate functions, thus extending a result of Comets, Gantert, and Zeitouni for nearest-neighbor RWRE on $\mathbb{Z}