Softcover ISBN:  9780821846247 
Product Code:  SURV/114.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413415 
Product Code:  SURV/114.S.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821846247 
eBook: ISBN:  9781470413415 
Product Code:  SURV/114.S.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 
Softcover ISBN:  9780821846247 
Product Code:  SURV/114.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413415 
Product Code:  SURV/114.S.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821846247 
eBook ISBN:  9781470413415 
Product Code:  SURV/114.S.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 114; 2005; 242 ppMSC: Primary 30; 31; 60; 81; 82
Theoretical physicists have predicted that the scaling limits of many twodimensional lattice models in statistical physics are in some sense conformally invariant. This belief has allowed physicists to predict many quantities for these critical systems. The nature of these scaling limits has recently been described precisely by using one wellknown tool, Brownian motion, and a new construction, the SchrammLoewner evolution (SLE).
This book is an introduction to the conformally invariant processes that appear as scaling limits. The following topics are covered: stochastic integration; complex Brownian motion and measures derived from Brownian motion; conformal mappings and univalent functions; the Loewner differential equation and Loewner chains; the SchrammLoewner evolution (SLE), which is a Loewner chain with a Brownian motion input; and applications to intersection exponents for Brownian motion. The prerequisites are firstyear graduate courses in real analysis, complex analysis, and probability. The book is suitable for graduate students and research mathematicians interested in random processes and their applications in theoretical physics.
ReadershipGraduate students and research mathematicians interested in random processes and their applications in theoretical physics.

Table of Contents

Chapters

1. Stochastic calculus

2. Complex Brownian motion

3. Conformal mappings

4. Loewner differential equation

5. Brownian measures on paths

6. SchrammLoewner evolution

7. More results about $SLE$

8. Brownian intersection exponent

9. Restriction measures


Additional Material

Reviews

This nice book celebrates the fruitful marriage of Brownian motion and complex analysis.
Zentralblatt MATH 
This book gives a nice and systematic introduction to the contiuous time conformally invariant processes in the plane, assuming only knowledge of first year graduate real analysis, complex analysis and probability theory...This books is very well written, and can also be used as a graudate textbook for a topic course on SLE.
Mathematical Reviews


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
Theoretical physicists have predicted that the scaling limits of many twodimensional lattice models in statistical physics are in some sense conformally invariant. This belief has allowed physicists to predict many quantities for these critical systems. The nature of these scaling limits has recently been described precisely by using one wellknown tool, Brownian motion, and a new construction, the SchrammLoewner evolution (SLE).
This book is an introduction to the conformally invariant processes that appear as scaling limits. The following topics are covered: stochastic integration; complex Brownian motion and measures derived from Brownian motion; conformal mappings and univalent functions; the Loewner differential equation and Loewner chains; the SchrammLoewner evolution (SLE), which is a Loewner chain with a Brownian motion input; and applications to intersection exponents for Brownian motion. The prerequisites are firstyear graduate courses in real analysis, complex analysis, and probability. The book is suitable for graduate students and research mathematicians interested in random processes and their applications in theoretical physics.
Graduate students and research mathematicians interested in random processes and their applications in theoretical physics.

Chapters

1. Stochastic calculus

2. Complex Brownian motion

3. Conformal mappings

4. Loewner differential equation

5. Brownian measures on paths

6. SchrammLoewner evolution

7. More results about $SLE$

8. Brownian intersection exponent

9. Restriction measures

This nice book celebrates the fruitful marriage of Brownian motion and complex analysis.
Zentralblatt MATH 
This book gives a nice and systematic introduction to the contiuous time conformally invariant processes in the plane, assuming only knowledge of first year graduate real analysis, complex analysis and probability theory...This books is very well written, and can also be used as a graudate textbook for a topic course on SLE.
Mathematical Reviews