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Variational Formulas and Cocycle solutions for Directed Polymer and Percolation Models
We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting…
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Stationary cocycles and Busemann functions for the corner growth model
We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable…
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Geodesics and the competition interface for the corner growth model
We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable…
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Ratios of partition functions for the log-gamma polymer
We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition in-…
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Large deviation rate functions for the partition function in a log-gamma distributed random potential
We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the…
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Solvable non-Markovian dynamic network.
TLDR
The analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times.
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Last passage percolation in an exponential environment with discontinuous rates
We prove a strong law of large numbers for directed last passage times in an independent but inhomogeneous exponential environment. Rates for the exponential random variables are obtained from a…
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Stationary cocycles for the corner growth model
We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable…
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The Mathematics of Human Contact: Developing a Model for Social Interaction in School Children
TLDR
This article focuses on link- and node-level statistics, such as the on- and off-durations of links as well as the activity potential of nodes and links, with the aim of combining this contact pattern model with epidemic models in future work.
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Parenting and children’s adjustment problems: the mediating role of self-esteem and peer relations
ABSTRACT The aim of this study was to investigate the impact of parental and personal characteristics on children’s internalizing/externalizing problems. Further, this study aimed to examine personal…
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