Electrical resistance of the low dimensional critical branching random walk

We show that the electrical resistance between the origin and generation n of the incipient infinite oriented branching random walk in dimensions d<6 is O(n^{1-alpha}) for some universal constant alpha>0. This answers a question of Barlow, J\'arai, Kumagai and Slade [2].Comment: 44 pages, 3 figure

Migrant workers and human resource development practices in the hotel sector: a case of Cyprus

Purpose: This paper aims to investigate the human resource development (HRD) practices amongst migrant workers using a cross-national survey. The literature review has shown that there is a need to provide a comprehensive understanding of the significance of HRD in the hotel sector and its role in developing migrant workers skills. Moreover, hotels that have training and development opportunities tend to support their employees in training their people-to-people and other soft skills. Design/methodology/approach: This study adopted a quantitative approach using a self-administered questionnaire, employing a purposive sampling strategy to target key participants (hotel managers/supervisor/owners) across Cyprus. Findings: The findings show that most hotels only provide operational, informal level training to all their migrant workers. The key findings present a sector that currently does not plan for sustainable HRD practices and learning with casualisation being the dominant strategy to cope with changing demand for labour. Those few hotels that do have long-term HRD practices have seen an impact on their organisational performance as well as increased migrant workers skills. Practical implications: In practice, Cypriot hotels need to focus their attention on their long-term strategic goals. The development of their migrant employees may help enhance organisational performance in the long-term. However, further research is needed to explore current perceptions amongst migrant workers and how they perceive their long-term role in the industry. Originality/value: This paper contributes to the existing HRD literature since the training and development of migrant employees in Cypriot hotels have not been researched during the recession. HRD insights will enable policy makers and employers to improve current training infrastructure for migrant workers and add to the debate around the importance of HRD strategy in advancing organisational performance in such a transformational business environment

Geometric and spectral properties of causal maps

We study the random planar map obtained from a critical, finite variance, Galton-Watson plane tree by adding the horizontal connections between successive vertices at each level. This random graph is closely related to the well-known causal dynamical triangulation that was introduced by Ambj{\o}rn and Loll and has been studied extensively by physicists. We prove that the horizontal distances in the graph are smaller than the vertical distances, but only by a subpolynomial factor: The diameter of the set of vertices at level $n$ is both $o(n)$ and $n^{1-o(1)}$. This enables us to prove that the spectral dimension of the infinite version of the graph is almost surely equal to 2, and consequently that the random walk is diffusive almost surely. We also initiate an investigation of the case in which the offspring distribution is critical and belongs to the domain of attraction of an $\alpha$-stable law for $\alpha \in (1,2)$, for which our understanding is much less complete.Institut Universitaire de France, ANR Graal (ANR-14-CE25-0014), ANR Liouville (ANR-15-CE40-0013), ERC GeoBrown, ISF grant 1207/15 and ERC grant 676970 RandGeom

Students’ perception towards hospitality education: an Anglo-Cypriot critical study

The study investigates hospitality students' attitude towards hospitality education and hospitality careers. A qualitative approach was adapted to record students' attitude in the UK and Cyprus. The findings revealed that participants share common concerns and expectations regarding hospitality education and careers. A number of cognitive-person and external variables are perceived to act as influencing factors on hospitality education and careers, raising questions with regard to the student preparedness for the industry. This study provides a theoretical underpinning to hospitality literature that can be used to further fruitful thinking with implications for practice and further research

Unimodular hyperbolic triangulations: circle packing and random walk

We show that the circle packing type of a unimodular random plane triangulation is parabolic if and only if the expected degree of the root is six, if and only if the triangulation is amenable in the sense of Aldous and Lyons [1]. As a part of this, we obtain an alternative proof of the Benjamini–Schramm Recurrence Theorem [19]. Secondly, in the hyperbolic case, we prove that the random walk almost surely converges to a point in the unit circle, that the law of this limiting point has full support and no atoms, and that the unit circle is a realisation of the Poisson boundary. Finally, we show that the simple random walk has positive speed in the hyperbolic metric.OA is supported in part by NSERC. AN is supported by the Israel Science Foundation Grant 1207/15 as well as NSERC and NSF grants. GR is supported in part by the Engineering and Physical Sciences Research Council under Grant EP/103372X/1

Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time

For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (2007). This improvement finally settles a conjecture by Aizenman (1997) about the role of boundary conditions in critical high-dimensional percolation, and it is a key step in deriving further properties of critical percolation on the torus. Indeed, a criterion of Nachmias and Peres (2008) implies appropriate bounds on diameter and mixing time of the largest clusters. We further prove that the volume bounds apply also to any finite number of the largest clusters. The main conclusion of the paper is that the behavior of critical percolation on the high-dimensional torus is the same as for critical Erdos-Renyi random graphs. In this updated version we incorporate an erratum to be published in a forthcoming issue of Probab. Theory Relat. Fields. This results in a modification of Theorem 1.2 as well as Proposition 3.1.Comment: 16 pages. v4 incorporates an erratum to be published in a forthcoming issue of Probab. Theory Relat. Field

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

Line managers' perceptions of diversity management: insights from a social exchange theory perspective

Purpose: Drawing on the social exchange theory, this study aims to explore line managers' perceptions of diversity management, as well as their perceptions of their role and responsibilities in shaping and implementing diversity practices. The senior management's leadership support, as it is perceived by line managers, in assisting them to manage diversity successfully is also examined. Design/methodology/approach: Semi-structured interviews with 51 line managers across different sectors in the UK were conducted to address the following three research questions. First, how do line managers perceive diversity management? Second, what are the actual roles and responsibilities of line managers in shaping diversity practices' implementation? Third, how do leadership interactions within the organisation influence line managers' perceptions of diversity practices? Findings: Line managers present high levels of personal determination and commitment towards diversity supplemented by a consensus on the strategic role of leadership in relation to diversity management. In addition, poor levels of organisational support, leadership values and style are identified; all highly related to their ability to deliver results and, most importantly, to form effective relationships in the workplace. Research limitations/implications: Data included line managers' views but not senior managers' perspectives, thus limiting the study in identifying the holistic impact of social exchanges in shaping effective relations. In addition, quantitative research could test and enhance the generalisability of existing findings. Practical implications: Investing in social relationships can positively influence line managers' ability to deliver results. Action is required at the organisational level by senior management to support and recognise line managers' critical roles to enable them to apply and promote diversity management. Originality/value: These findings address a theoretical gap relating to the evaluation of the critical role played by line managers in the delivery of diversity practices. The study further demonstrates how social exchange relationships can influence line managers' perceptions of diversity management, an unexplored area within the diversity literature