A Random Tiling Model for Two-Dimensional Electrostatics

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $30.00
Usually ships in 1-2 business days
(Save 54%)
Other sellers (Paperback)
  • All (3) from $30.00   
  • New (2) from $30.00   
  • Used (1) from $182.99   
Close
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any BN.com coupons and promotions
$30.00
Seller since 2005

Feedback rating:

(329)

Condition:

New — never opened or used in original packaging.

Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift.

Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage.

Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item.

Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer.

New
2005 Softcover New

Ships from: Hillsboro, OR

Usually ships in 1-2 business days

  • Standard, 48 States
  • Standard (AK, HI)
  • Express, 48 States
  • Express (AK, HI)
$59.00
Seller since 2007

Feedback rating:

(420)

Condition: New
Brand new. We distribute directly for the publisher. The two parts of this Memoir contain two separate but closely related papers. In the paper in Part A we study the correlation ... of holes in random lozenge (i.e., unit rhombus) tilings of the triangular lattice. More precisely, we analyze the joint correlation of these triangular holes when their complement is tiled uniformly at random by lozenges. We determine the asymptotics of the joint correlation (for large separations between the holes) in the case when one of the holes has side 1, all remaining holes have side 2, and the holes are distributed symmetrically with respect to a symmetry axis. Our result has a striking physical interpretation. If we regard the holes as electrical charges, with charge equal to the difference between the number of down-pointing and up-pointing unit triangles in a hole, the logarithm of the joint correlation behaves exactly like the electrostatic potential energy of this two-dimensional electrostatic system: it is obtained by a Superposition Principle from the interaction of all pairs, and the pair interactions are according to Coulomb's law. The starting point of the proof is a pair of exact lozenge tiling enumeration results for certain regions on the triangular lattice, presented in the second paper.The paper in Part B was originally motivated by the desire to find a multi-parameter deformation of MacMahon's simple product formula for the number of plane partitions contained in a given box. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths $a,b,c,a,b,c$ (in cyclic order) and angles of 120 degrees. We present a generalization in the case $b=c$ by giving simple product formulas enumerating lozenge tilings of regions obtained from a hexagon of side-lengths $a,b+k,b,a+k,b,b+k$ (where $k$ is an arbitrary non-negative integer) and angles of 120 degrees by removing certain triangular regions along its symmetry axis. The paper in Part A uses these formulas to deduce that in the scaling limi Read more Show Less

Ships from: Boonsboro, MD

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
  • Express, 48 States
  • Express (AK, HI)
Page 1 of 1
Showing All
Close
Sort by

More About This Textbook

Overview

The two parts of this Memoir contain two separate but closely related papers. In the paper in Part A we study the correlation of holes in random lozenge (i.e., unit rhombus) tilings of the triangular lattice. More precisely, we analyze the joint correlation of these triangular holes when their complement is tiled uniformly at random by lozenges. We determine the asymptotics of the joint correlation (for large separations between the holes) in the case when one of the holes has side 1, all remaining holes have side 2, and the holes are distributed symmetrically with respect to a symmetry axis. Our result has a striking physical interpretation. If we regard the holes as electrical charges, with charge equal to the difference between the number of down-pointing and up-pointing unit triangles in a hole, the logarithm of the joint correlation behaves exactly like the electrostatic potential energy of this two-dimensional electrostatic system: it is obtained by a Superposition Principle from the interaction of all pairs, and the pair interactions are according to Coulomb's law. The starting point of the proof is a pair of exact lozenge tiling enumeration results for certain regions on the triangular lattice, presented in the second paper. The paper in Part B was originally motivated by the desire to find a multi-parameter deformation of MacMahon's simple product formula for the number of plane partitions contained in a given box. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths $a,b,c,a,b,c$ (in cyclic order) and angles of 120 degrees. We present a generalization in the case $b=c$ by giving simple product formulas enumerating lozenge tilings of regions obtained from a hexagon of side-lengths $a,b+k,b,a+k,b,b+k$ (where $k$ is an arbitrary non-negative integer) and angles of 120 degrees by removing certain triangular regions along its symmetry axis. The paper in Part A uses these formulas to deduce that in the scaling limit the correlation of the holes is governed by two dimensional electrostatics.

Read More Show Less

Product Details

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)