
Tue 25 Nov 2014, 4:00pm
SPECIAL
One Time Event
Graduate Student Center, Room 203

Doctoral Exam

Graduate Student Center, Room 203
Tue 25 Nov 2014, 4:00pm6:30pm
Details
Spin systems such as the Ising model are central topics in statistical mechanics and probability theory. In the late 1960s Symanzik made the important discovery that properties of spin systems could be expressed in terms of the behaviour of random walks. This thesis contributes to the understanding of these connections by developing and analyzing random walk representations of graphical models arising in statistical mechanics.
Concretely, the results of this thesis can be divided into two parts. The first part is a lace expansion analysis of a model called loopweighted walk. Loopweighted walk is a nonMarkovian model of random walks that are discouraged (or encouraged), depending on the value of a parameter, from completing loops. The model arises naturally as a random walk representation of correlations in a statistical mechanics model called the cycle gas. A challenging aspect of this model is that it is not repulsive, meaning the weight of the future of a walk may either increase or decrease if the past is forgotten. Loopweighted walk is the first finite range walk model with this property to be analyzed with lace expansion techniques.
The second part of this thesis is an essentially elementary derivation of a random walk representation for the partition function of the Ising model on any finite graph. Such representations have a long history for planar graphs. For nonplanar graphs the additional ingredient needed is a way to compute the intersection numbers of curves on surfaces. The representations for nonplanar graphs lead to random walk representations of spinspin correlation functions that were previously unknown.
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Case Western

Wed 3 Dec 2014, 3:00pm
One Time Event
ESB 4127 (host: UAlberta)

TBA

ESB 4127 (host: UAlberta)
Wed 3 Dec 2014, 3:00pm4:00pm
Details
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Sat 10 Jan 2015, 9:00am
SPECIAL
One Time Event
To Be Announced

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To Be Announced
Sat 10 Jan 2015, 9:00am12:00pm
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Sat 10 Jan 2015, 1:00pm
SPECIAL
One Time Event
To Be Announced

Differential Equations  Qualifying Exams

To Be Announced
Sat 10 Jan 2015, 1:00pm4:00pm
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Sat 10 Jan 2015, 1:00pm
SPECIAL
One Time Event
To Be Announced Later

Algebra Qualifying Exams

To Be Announced Later
Sat 10 Jan 2015, 1:00pm4:00pm
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